Strong $L^ p$-solutions of the Navier-Stokes equation in $R^ m$, with applications to weak solutions

DOI10.1007/BF01174182zbMath0545.35073MaRDI QIDQ797057

Publication date: 1984

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173504

zbMATH Keywords

uniqueness local existence decays Leray's structure theorem turbulent solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Navier-Stokes equations (35Q30)

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Navier-Stokes flows in the half-space ⋮ Global strong solution for the density dependent incompressible viscoelastic fluids in the critical $L^p$ framework ⋮ A regularity criterion for the Navier-Stokes equations in terms of one directional derivative of the velocity ⋮ The role of the Besov space ${\mathbf B}_{\infty}^{-1,\infty}$ in the control of the eventual explosion in finite time of the regular solutions of the Navier-Stokes equations ⋮ Existence and uniqueness theorem on mild solutions to the Keller-Segel system coupled with the Navier-Stokes fluid ⋮ On local uniqueness of weak solutions of the Navier--Stokes system with bounded initial data. ⋮ Weak and strong solutions for the incompressible Navier-Stokes equations with damping ⋮ On regularity criteria for the $n$-dimensional Navier-Stokes equations in terms of the pressure ⋮ The Navier-Stokes equations in the critical Morrey-Campanato space ⋮ On local uniqueness of weak solutions to the Navier-Stokes system with $\mathrm{BMO}^{-1}$ initial datum ⋮ The Picard iterates for the Navier-Stokes equations in $L^3(\mathbb R^3)$ ⋮ Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces ⋮ Remark on the regularities of Kato's solutions to Navier-Stokes equations with initial data in $L^d(\mathbb R^d)$ ⋮ Global solvability of the Cauchy problem for the Navier-Stokes equation in $\mathbb {R}^3$ for some class of initial data ⋮ On the decay of higher order derivatives of solutions to Ladyzhenskaya model for incompressible viscous flows ⋮ Partial regularity of solutions to the four-dimensional Navier-Stokes equations at the first blow-up time ⋮ Asymptotic behaviour in $L^ r$ for weak solutions of the Navier-Stokes equations in exterior domains ⋮ Regularity results of axisymmetric solutions for the Navier-Stokes system. ⋮ $L^ 2$-decay for Navier-Stokes flows in unbounded domains, with application to exterior stationary flows ⋮ Stability of 2D incompressible flows in $\mathbb R^3$ ⋮ The drift-diffusion system in two-dimensional critical Hardy space ⋮ New results of general $n$-dimensional incompressible Navier-Stokes equations ⋮ A global solution for the $t^{\alpha }$-type Navier-Stokes equations ⋮ Navier-Stokes equations and nonlinear heat equations in modulation spaces with negative derivative indices ⋮ On the generalized self-similar singularities for the Euler and the Navier-Stokes equations ⋮ Ill-posedness of the 3D-Navier-Stokes equations in a generalized Besov space near $\mathrm{BMO}^{-1}$ ⋮ The Fujita-Kato approach to the Navier-Stokes equations in the rotational framework ⋮ A singular parabolic equation with logarithmic nonlinearity and $L^p$-initial data ⋮ Optimal weighted estimates of the flows in exterior domains ⋮ Generalized Navier-Stokes equations with initial data in local $Q$-type spaces ⋮ Well-posedness of a dissipative nonlinear electrohydrodynamic system in modulation spaces ⋮ Global well-posedness for the 2D critical dissipative quasi-geostrophic equation ⋮ Existence and generalized Gevrey regularity of solutions to the Kuramoto-Sivashinsky equation in $\mathbb R^n$ ⋮ Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equation ⋮ On upper and lower bounds of higher order derivatives for solutions to the 2D micropolar fluid equations ⋮ Ill-posedness of the Navier-Stokes equations in a critical space in 3D ⋮ The second iterate for the Navier-Stokes equation ⋮ Temporal and spatial decays for the Navier-Stokes equations ⋮ A critical functional framework for the inhomogeneous Navier-Stokes equations in the half-space ⋮ A nonlinear equation in Banach spaces and applications to the well-posedness of Cauchy problems ⋮ On the weighted decay for solutions of the Navier-Stokes system ⋮ On the uniqueness of time-periodic solutions to the Navier-Stokes equations in unbounded domains ⋮ On weighted-norm estimates for nonstationary incompressible Navier-Stokes flows in a 3D exterior domain ⋮ Wellposedness and stability results for the Navier-Stokes equations in $\mathbb R^3$ ⋮ Decay properties of strong solutions for the Navier-Stokes equations in two-dimensional unbounded domains ⋮ Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations ⋮ Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation ⋮ Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains ⋮ Analysis of a Ladyzhenskaya model for incompressible viscous flow ⋮ On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations ⋮ Beale-Kato-Majda type condition for Burgers equation ⋮ Global $L^ n$-solution and its decay property for the Navier-Stokes equations in half-space $R^ n_ +$ ⋮ Weighted estimates for nonstationary Navier-Stokes equations ⋮ On the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations ⋮ Algebraic $L^ 2$ decay for Navier-Stokes flows in exterior domains ⋮ Global existence and asymptotic behavior of self-similar solutions for the Navier-Stokes-Nernst-Planck-Poisson system in $\mathbb R^3$ ⋮ Stability of plane Couette flows with respect to small periodic perturbations ⋮ Well-posedness for the incompressible magneto-hydrodynamic system on modulation spaces ⋮ Spatial stability of 3D exterior stationary Navier-Stokes flows ⋮ A note on the regularity criterion in terms of pressure for the Navier-Stokes equations ⋮ Well-posedness of a semilinear heat equation with weak initial data ⋮ Long time behavior of solutions to 3D generalized MHD equations ⋮ Decay estimates of gradient of a generalized Oseen evolution operator arising from time-dependent rigid motions in exterior domains ⋮ On optimal initial value conditions for local strong solutions of the Navier-Stokes equations ⋮ Global solutions of the Navier-Stokes equations in thin three-dimensional domains ⋮ Exponential stability and regularity of compressible viscous micropolar fluid with cylinder symmetry ⋮ Estimates for the Navier-Stokes equations in the half-space for nonlocalized data ⋮ The initial boundary value problem for Navier-Stokes equations ⋮ Uniqueness of solutions of Navier-Stokes equations in Morrey-Campanato spaces ⋮ Global solutions to the generalized Leray-$\alpha$ system with non-$L^2(\mathbb{R}^n)$ initial data ⋮ Scaling in nonlinear parabolic equations ⋮ Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains ⋮ Weak solutions of Navier-Stokes equations ⋮ Global stability of large solutions to the 3D Navier-Stokes equations ⋮ Solutions for semilinear parabolic equations in $L^ p$ and regularity of weak solutions of the Navier-Stokes system ⋮ Two-dimensional Navier-Stokes flow in unbounded domains ⋮ Some results on the asymptotic behaviour of weak Hopf solutions of the Navier-Stokes equations in unbounded domains ⋮ Square-integrable solutions to a family of nonlinear Schrödinger equations from nonlinear quantum theory ⋮ Gevrey regularity and existence of Navier-Stokes-Nernst-Planck-Poisson system in critical Besov spaces ⋮ $L^2$-asymptotic stability of singular solutions to the Navier-Stokes system of equations in $\mathbb R^3$ ⋮ Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent magnetohydrodynamic equations with vacuum ⋮ The well-posedness of the incompressible magnetohydrodynamic equations in the framework of Fourier-Herz space ⋮ Global well-posedness of incompressible Navier-Stokes equations with two slow variables ⋮ Global strong solution to the 3D incompressible magnetohydrodynamic system in the scaling invariant Besov-Sobolev-type spaces ⋮ Global solution of the 3D incompressible Navier-Stokes equations in the Besov spaces $\dot{R}_{r_{1},r_{2},r_{3}}^{\sigma,1}$ ⋮ Lower bounds on blow-up of solutions for magneto-micropolar fluid systems in homogeneous Sobolev spaces ⋮ $\mathbb{L}^p$-solutions of the stochastic Navier-Stokes equations subject to Lévy noise with $\mathbb{L}^m(\mathbb{R}^m)$ initial data ⋮ Global existence for an inhomogeneous fluid ⋮ Global well-posedness of the three dimensional incompressible anisotropic Navier-Stokes system ⋮ On the regularity set and angular integrability for the Navier-Stokes equation ⋮ Stability of time periodic solution of the Navier-Stokes equation on the half-space under oscillatory moving boundary condition ⋮ Existence and uniqueness of solutions for Navier-Stokes equations with hyper-dissipation in a large space ⋮ Global stability of homogeneous steady states in scaling-invariant spaces for a Keller-Segel-Navier-Stokes system ⋮ Asymptotic energy concentration in the phase space of the weak solutions to the Navier-Stokes equations ⋮ Global well-posedness for the viscous primitive equations of geophysics ⋮ Well-posedness of quasi-geostrophic equations with data in Besov-$Q$ spaces ⋮ Existence of strong solutions and decay of turbulent solutions of Navier-Stokes flow with nonzero Dirichlet boundary data ⋮ Large time decay of solutions to the Boussinesq system with fractional dissipation ⋮ Periodic solutions to Navier-Stokes equations on non-compact Einstein manifolds with negative curvature ⋮ Maximum norm estimates of the solution of the Navier-Stokes equations in the halfspace with bounded initial data ⋮ Global well-posedness and exponential stability of 3D Navier-Stokes equations with density-dependent viscosity and vacuum in unbounded domains ⋮ Global solution in critical spaces to the compressible Oldroyd-B model with non-small coupling parameter ⋮ Existence of a stationary Navier-Stokes flow past a rigid body, with application to starting problem in higher dimensions ⋮ Well-posedness for the Navier-Stokes equations with datum in the Sobolev spaces ⋮ Existence and analyticity of mild solutions for the 3D rotating Navier-Stokes equations ⋮ Navier-Stokes equation in super-critical spaces $E_{p,q}^s$ ⋮ Nonstationary Navier-Stokes equations with singular time-dependent external forces ⋮ Well-posedness and scattering for the Boltzmann equations: soft potential with cut-off ⋮ Navier-Stokes regularity criteria in sum spaces ⋮ Regular sets and an $\varepsilon $-regularity theorem in terms of initial data for the Navier-Stokes equations ⋮ Time periodic strong solutions to the incompressible Navier-Stokes equations with external forces of non-divergence form ⋮ Global well-posedness and long time decay of the 3D Boussinesq equations ⋮ Boundedness, almost periodicity and stability of certain Navier-Stokes flows in unbounded domains ⋮ Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces ⋮ Periodicity of inhomogeneous trajectories and applications ⋮ Time decay rate of global strong solutions to nematic liquid crystal flows in $\mathbb{R}_+^3$ ⋮ Solvability for a drift-diffusion system with Robin boundary conditions ⋮ $L^{3,\infty}$ solutions of the liquid crystals system ⋮ Well/ill-posedness for the dissipative Navier-Stokes system in generalized Carleson measure spaces ⋮ Asymptotic stability of Landau solutions to Navier-Stokes system under $L^p$-perturbations ⋮ Global strong solutions to 3-D Navier-Stokes system with strong dissipation in one direction ⋮ Blow ups of complex solutions of the 3D Navier-Stokes system and renormalization group method ⋮ Weighted estimate of the asymptotic profiles of the Navier-Stokes flow in $\mathbb R^n$ ⋮ Asymptotic behavior of solutions to viscous conservation laws with slowly varying external forces ⋮ Estimates of perturbed Oseen semigroups and their applications to the Navier-Stokes system in $\mathbb R^n$ ⋮ Estimates for operators on weighted Morrey spaces and their applications to nondivergence elliptic equations ⋮ Space-time regularity of the Koch \& Tataru solutions to Navier-Stokes equations ⋮ Global wellposedness for a certain class of large initial data for the 3D Navier-Stokes equations ⋮ Regularity criteria with angular integrability for the Navier-Stokes equation ⋮ Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions ⋮ Space-time estimates of mild solutions of a class of higher-order semilinear parabolic equations in $L^{p}$ ⋮ An application of weighted Hardy spaces to the Navier-Stokes equations ⋮ Nonexistence of asymptotically self-similar singularities in the Euler and the Navier-Stokes equations ⋮ Blow-up criterion of strong solutions to the Navier-Stokes equations in Besov spaces with negative indices ⋮ Weak Morrey spaces and strong solutions to the Navier-Stokes equations ⋮ Decay rate of solutions of Navier-Stokes equations in 3-dimensional half space ⋮ Decay of weak solutions to the 2D dissipative quasi-geostrophic equation ⋮ Well-posedness for the drift-diffusion system in $L^p$ arising from the semiconductor device simulation ⋮ Local existence and Gevrey regularity of 3-D Navier-Stokes equations with $\ell_p$ initial data ⋮ Pressure integrability conditions for uniqueness of mild solutions of the Navier--Stokes system ⋮ Multipliers, paramultipliers, and weak-strong uniqueness for the Navier-Stokes equations ⋮ The self-similar solution to some nonlinear integro-differential equations corresponding to fractional order time derivative ⋮ Global well-posedness of the three dimensional magnetohydrodynamics equations ⋮ Well-posedness for the 3D incompressible nematic liquid crystal system in the critical $L^p$ framework ⋮ Regularity criterion for 3D MHD fluid passing through the porous medium in terms of gradient pressure ⋮ The Navier-Stokes equations with data in $bmo^{-1}$ ⋮ A regularity criterion for the Navier-Stokes equation involving only the middle eigenvalue of the strain tensor ⋮ Global solutions of 3-d Navier-Stokes system with small unidirectional derivative ⋮ Bilinear estimates and uniqueness for Navier-Stokes equations in critical Besov-type spaces ⋮ Critical and super-critical abstract parabolic equations ⋮ Time decay rates of the $L^3$-norm for strong solutions to the Navier-Stokes equations in $\mathbb{R}^3$ ⋮ The 3D Navier-Stokes equations: invariants, local and global solutions ⋮ Two scenarios on a potential smoothness breakdown for the three-dimensional Navier-Stokes equations ⋮ Local well-posedness for Navier-Stokes equations with a class of ill-prepared initial data ⋮ Exact solutions for the Cauchy problem to the 3D spherically symmetric incompressible Navier-Stokes equations ⋮ Asymptotic behavior of weak solutions to the damped Navier-Stokes equations ⋮ Commutator estimate and its application to regularity criteria of the dissipative quasi-geostrophic equation ⋮ Remarks on global well-posedness of mild solutions to the three-dimensional Boussinesq equations ⋮ Upper and lower bounds of decay rates for $\dot{H}^{- \frac{1}{2}}$ weak solutions of the surface quasi-geostrophic equation ⋮ A new path to the non blow-up of incompressible flows ⋮ Blowup criterion for Navier-Stokes equation in critical Besov space with spatial dimensions $d \geq 4$ ⋮ Local and global strong solutions to the stochastic incompressible Navier-Stokes equations in critical Besov space ⋮ Discontinuity of weak solutions to the 3D NSE and MHD equations in critical and supercritical spaces ⋮ On the existence and uniqueness of mild and strong solutions of a generalized nonlinear heat equation ⋮ Sharp well-posedness and ill-posedness of the three-dimensional primitive equations of geophysics in Fourier-Besov spaces ⋮ On the continuity of the solutions to the Navier-Stokes equations with initial data in critical Besov spaces ⋮ Space-time regularity for the three dimensional Navier-Stokes and MHD equations ⋮ $L^p$-solutions of the Navier-Stokes equation with fractional Brownian noise ⋮ On analyticity rate estimates of the solutions to the Navier--Stokes equations in Bessel-potential spaces ⋮ Well-posedness and decay of solutions for three-dimensional generalized Navier-Stokes equations ⋮ Space-time derivative estimates of the Koch-Tataru solutions to the nematic liquid crystal system in Besov spaces ⋮ Heat and Navier-Stokes equations in supercritical function spaces ⋮ On existence and scattering theory for the Klein-Gordon-Schrödinger system in an infinite $L^{2}$-norm setting ⋮ Space-time regularity of the solutions to MHD equations with small rough data ⋮ Global well-posedness for the 3-D incompressible MHD equations in the critical Besov spaces ⋮ Mild solutions to the time fractional Navier-Stokes equations in $\mathbb{R}^N$ ⋮ Local analyticity radii of solutions to the 3D Navier-Stokes equations with locally analytic forcing ⋮ On the smoothing effect in the kinematic dynamo equations in critical spaces ⋮ Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces ⋮ Temporal decay of strong solutions for generalized Newtonian fluids with variable power-law index ⋮ Zero-Mach limit of the compressible Navier–Stokes–Korteweg equations ⋮ On the strong solution of 3D non-isothermal Navier–Stokes–Cahn–Hilliard equations ⋮ Global well-posedness of perturbed Navier–Stokes system around Landau solutions ⋮ Quantitative bounds for critically bounded solutions to the Navier-Stokes equations ⋮ Aspects of PDEs Related to Fluid Flows ⋮ Strong solutions of the Navier-Stokes equation in Morrey spaces ⋮ Low Mach number limit for viscous compressible flows ⋮ Well-posedness for the Boussinesq system in critical spaces via maximal regularity ⋮ Convergence of approximating solutions of the Navier-Stokes equations in $\mathbb{R}^n$ ⋮ Global existence of free-energy solutions to the 2D Patlak-Keller-Segel-Navier-Stokes system with critical and subcritical mass ⋮ Recurrent motion of stochastic Navier–Stokes equations with Coriolis force ⋮ Vortex Filament Solutions of the Navier‐Stokes Equations ⋮ Well-posedness of mild solutions for the fractional Navier-Stokes equations in Besov spaces ⋮ Well-posedness and stability of solutions for the 3-D generalized micropolar system in Fourier-Besov-Morrey spaces ⋮ Global well-posedness of the Navier-Stokes equations in homogeneous Besov spaces on the half-space ⋮ Stability of Navier-Stokes system with singular external force in Fourier-Herz space ⋮ The continuous dependence for the Navier-Stokes equations in $\dot{B}^{\frac{d}{p}-1}_{p,r}$ ⋮ Global existence and spatial analyticity for a nonlocal flux with fractional diffusion ⋮ Distribution of large value points via frequency and wellposedness of Navier-Stokes equations ⋮ (X,Y,φ)-Stable semigroups, periodic solutions, and applications ⋮ Logarithmically improved extension criteria involving the pressure for the Navier–Stokes equations in Rn$\mathbb {R}^{n}$ ⋮ Maximal regularity for the Cauchy problem of the heat equation in BMO ⋮ On regularity of weak solutions for the Navier–Stokes equations in general domains ⋮ Motion of rigid bodies of arbitrary shape in a viscous incompressible fluid: wellposedness and large time behaviour ⋮ Regularity criterion in terms of the oscillation of pressure for the 3D Navier-Stokes equations ⋮ On the instantaneous radius of analyticity of $L^p$ solutions to 3D Navier-Stokes system ⋮ Numerical investigations of non-uniqueness for the Navier-Stokes initial value problem in borderline spaces ⋮ Large time behavior of weak solutions to the surface growth equation ⋮ On exponential splitting methods for semilinear abstract Cauchy problems ⋮ Remarks on regularity criteria for the 3d Navier-Stokes equations ⋮ Mild solutions and spacetime integral bounds for Stokes and Navier-Stokes flows in Wiener amalgam spaces ⋮ Navier-Stokes equation with hereditary viscosity and initial data in Besov-Morrey spaces ⋮ Existence and stability of $L^p$ solutions of the steady state magnetohydrodynamic equations with rough external forces ⋮ Sharp Nonuniqueness of Solutions to Stochastic Navier–Stokes Equations ⋮ Long time decay of solutions to the 3D incompressible Navier–Stokes equations with nonlinear damping ⋮ Globally well-posedness results of the fractional Navier-Stokes equations on the Heisenberg group ⋮ Anisotropically weighted Lq$L^q$‐Lr$L^r$ estimates of the Oseen semigroup in exterior domains, with applications to the Navier–Stokes flow past a rigid body ⋮ Global solution to the Cauchy problem of fractional drift diffusion system with power-law nonlinearity ⋮ Uniqueness and regularity of weak solutions of a fluid-rigid body interaction system under the Prodi-Serrin condition ⋮ Periodic motions of the non-autonomous Oseen-Navier-Stokes flows past a moving obstacle with data in $L^p$-spaces ⋮ An $\boldsymbol{L^1_{k}\cap L^{p}_{k}}$ Approach for the Non-Cutoff Boltzmann Equation in $\boldsymbol{\mathbb{R}^3}$ ⋮ Well-posedness for the Cahn-Hilliard-Navier-Stokes equations with random initial data ⋮ Smooth solution for incompressible Navier–Stokes equations with large initial ⋮ The global well-posedness of strong solutions to 2D MHD equations in Lei-Lin space ⋮ Middle frequency band and remark on Koch–Tataru’s iteration space ⋮ Forced Rapidly Dissipative Navier–Stokes Flows ⋮ Sharp ill-posedness for the non-resistive MHD equations in Sobolev spaces ⋮ Ricci curvature and the size of initial data for the Navier-Stokes equations on Einstein manifolds ⋮ Well-posedness of the three-dimensional axisymmetric incompressible magnetohydrodynamics system in the exterior of a cylinder ⋮ Gevrey class regularity and stability for the Debye-H¨uckel system in critical Fourier-Besov-Morrey spaces ⋮ Remarks on the Navier-Stokes equations in homogeneous and isotropic spacetimes ⋮ Scaling-invariant Serrin criterion via one velocity component for the Navier-Stokes equations ⋮ Unnamed Item ⋮ Time asymptotic profiles to the magneto-micropolar system ⋮ Liouville-type theorems for the Navier–Stokes equations ⋮ Sharp time decay rates of H ¹ weak solutions for the 2D MHD equations with linear damping velocity ⋮ Global regularity for solutions of the three dimensional Navier–Stokes equation with almost two dimensional initial data ⋮ On regularity criteria in terms of pressure for the Navier-Stokes equations in ℝ³ ⋮ Weak solutions for the Navier-Stokes equations with $B^{-1(\ln )}_{\infty \infty }+B_{X_r}^{-1+r,\frac{2}{1-r}}+L^2$B∞∞−1(ln)+BXr−1+r,21−r+L2 initial data ⋮ Navier–Stokes equations with external forces in Besov–Morrey spaces ⋮ Existence of transitions between stationary regimes of the Navier-Stokes equations in the entire space ⋮ Well-posedness for the Navier-Stokes equations ⋮ The existence of periodic solution and behavior of the generalized solution when $t\to+\infty$ of boundary problem of non-Newtonian fluids ⋮ Existence and asymptotic behavior for an incompressible Newtonian flow with intrinsic degree of freedom ⋮ Global-in-time solutions to three-dimensional magnetohydrodynamics equations with a class of large initial data ⋮ Weak solutions of the Navier-Stokes equations with test functions in the weak-$L^n$ space ⋮ Global large solutions to incompressible Navier‐Stokes equations with gravity ⋮ Stability of nontrivial solutions of the Navier-Stokes system on the three-dimensional torus ⋮ Asymptotic behavior for strong solutions of the Navier-Stokes equations with external forces ⋮ Non-Uniform Decay of MHD Equations With and Without Magnetic Diffusion ⋮ Regularity criterion in terms of pressure for the Navier-Stokes equations ⋮ Well-posedness of the fractional Ginzburg–Landau equation ⋮ Global mild solutions of Navier‐Stokes equations ⋮ Space-time decay estimates for the incompressible viscous resistive MHD and Hall-MHD equations ⋮ Well-posedness for the Navier-Stokes equations with datum in Sobolev-Fourier-Lorentz spaces ⋮ Stokes and Navier-Stokes problems with Navier-type boundary condition in L^p-spaces ⋮ On ratio improvement of Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system ⋮ Regularity Criterion for Solutions of Three-Dimensional Turbulent Channel Flows ⋮ Asymptotically self-similar global solutions for Hardy-Hénon parabolic systems ⋮ DYNAMICS AND UNIVERSALITY OF AN ISOTHERMAL COMBUSTION PROBLEM IN 2D ⋮ Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity ⋮ On the relation between very weak and Leray–Hopf solutions to Navier–Stokes equations ⋮ Some remarks about the possible blow-up for the Navier-Stokes equations ⋮ Decay characterization of solutions to dissipative equations ⋮ Global well-posedness of a dissipative system arising in electrohydrodynamics in negative-order Besov spaces ⋮ On the supnorm form of Leray’s problem for the incompressible Navier-Stokes equations ⋮ Existence and analyticity of Lei-Lin solution to the Navier-Stokes equations ⋮ On regularity criteria of the Navier–Stokes equations in bounded domains ⋮ Navier-Stokes Equations for Elliptic Complexes ⋮ Annihilation of slowly-decaying terms of Navier–Stokes flows by external forcing ⋮ On Some Classes of Time-Periodic Solutions for the Navier--Stokes Equations in the Whole Space ⋮ Remarks on logarithmical regularity criteria for the Navier–Stokes equations ⋮ Large time behavior for the incompressible magnetohydrodynamic equations in half-spaces ⋮ Well-posedness for fractional Navier-Stokes equations in the largest critical spaces Ḃ∞,∞−(2β−1)(Rn) ⋮ Besov-Morrey spaces: Function space theory and applications to non-linear PDE ⋮ The existence, uniqueness, and regularity for an incompressible Newtonian flow with intrinsic degree of freedom ⋮ GLOBAL EXISTENCE TO THE NAVIER–STOKES EQUATIONS THROUGH A SELF-SIMILAR-LIKE UPPER SOLUTION ⋮ Pressure regularity criteria of the three-dimensional micropolar fluid flows ⋮ A sharp decay result on strong solutions of the navier-stokes equations in the whole ⋮ Decay properties for the incompressible Navier-Stokes flows in a half space ⋮ Periodic and almost periodic evolution flows and their stability on non-compact Einstein manifolds and applications ⋮ Ill-posedness of the 3D incompressible hyperdissipative Navier–Stokes system in critical Fourier-Herz spaces ⋮ REGULARITY OF WEAK SOLUTIONS FOR THE NAVIER–STOKES EQUATIONS IN THE CLASS L^∞(BMO^-1) ⋮ On the blow-up criterion of magnetohydrodynamics equations in homogeneous Sobolev spaces ⋮ A new regularity criterion for strong solutions to the Ericksen–Leslie system ⋮ Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations ⋮ A Remark on Maximal Regularity of the Stokes Equations ⋮ On the Relation Between the Large Time Behavior of the Stokes Semigroup and the Decay of Steady Stokes Flow at Infinity ⋮ On two dimensional incompressible fluids ⋮ Weak Neumann implies Stokes ⋮ Decay properties of solutions to the incompressible magnetohydrodynamics equations in a half space ⋮ Bilinear estimate on tent-type spaces with application to the well-posedness of fluid equations ⋮ On the stability of global solutions to the three-dimensional Navier-Stokes equations ⋮ Boundedness of paraproducts on spaces of homogeneous type I ⋮ Selected Topics of Local Regularity Theory for Navier–Stokes Equations ⋮ From Newton to Navier–Stokes, or how to connect fluid mechanics equations from microscopic to macroscopic scales ⋮ Decay of solutions to the three-dimensional generalized Navier–Stokes equations ⋮ Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent Navier–Stokes equations with vacuum ⋮ Asymptotic behavior for the vorticity equations in dimensions two and three ⋮ Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data ⋮ Asymptotics of solutions to the Navier-Stokes system in exterior domains ⋮ Nematic Liquid Crystals in Lipschitz Domains ⋮ The cauchy problem for the critical nonlinear Schrödinger equation in Hs ⋮ Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations ⋮ Analysis on Morrey Spaces and Applications to Navier-Stokes and Other Evolution Equations ⋮ Existence of Regular Solutions of the Landau--Lifshitz--Gilbert Equation in 3D with Natural Boundary Conditions ⋮ Existence and Uniqueness of Weak Solutions to Viscous Primitive Equations for a Certain Class of Discontinuous Initial Data ⋮ On the blow-up criterion for the Navier-Stokes equations with critical time order ⋮ Large Time Behaviour of Solutions to the Navier-Stokes Equations in H Spaces ⋮ Global well-posedness of generalized magnetohydrodynamics equations in variable exponent Fourier-Besov-Morrey spaces ⋮ Large time behavior of solutions to the 3D rotating Navier-Stokes equations ⋮ On the incompressible limit of the compressible navier-stokes equations ⋮ Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations ⋮ Existence Theorems for the 3D–Navier–Stokes System Having as Initial Conditions Sums of Plane Waves ⋮ Forward Self-Similar Solutions to the Viscoelastic Navier--Stokes Equation with Damping ⋮ The role of the pressure in the regularity theory for the Navier-Stokes equations ⋮ Large time behaviour for the motion of a solid in a viscous incompressible fluid ⋮ The Green tensor of the nonstationary Stokes system in the half space ⋮ Self-similar solutions for navier-stokes equations in ⋮ Zeros of complex caloric functions and singularities of complex viscous Burgers equation ⋮ On stability of weak Navier–Stokes solutions with largeL^3,∞initial data ⋮ ON APPROXIMATE SOLUTIONS OF SEMILINEAR EVOLUTION EQUATIONS II: GENERALIZATIONS, AND APPLICATIONS TO NAVIER–STOKES EQUATIONS ⋮ Uniqueness and long time asymptotics for the parabolic–parabolic Keller–Segel equation ⋮ On the decay of higher-order norms of the solutions of Navier–Stokes equations ⋮ Global well posedness of 3D-NSE in Fourier-Lei-Lin spaces ⋮ Wellposedness for the magnetohydrodynamics equation in critical space ⋮ A remark for spatial analyticity around straining flows ⋮ Remark on a regularity criterion in terms of pressure for the Navier-Stokes equations ⋮ L 2 ( R n ) estimate of the solution to the Navier-Stokes equations with linearly growth initial data ⋮ Finite time blow up for a Navier-Stokes like equation ⋮ Axisymmetric flows in the exterior of a cylinder ⋮ Algebraic L2 decay for the solution to a class system of non-Newtonian fluid in Rn ⋮ Self-improving bounds for the Navier-Stokes equations ⋮ Remarks on regularity criterion for weak solutions to the Navier–Stokes equations in terms of the gradient of the pressure ⋮ Random data Cauchy theory for the incompressible three dimensional Navier–Stokes equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Global well-posedness for compressible Navier-Stokes equations with highly oscillating initial velocity ⋮ On the Instantaneous Spreading for the Navier–Stokes System in the Whole Space ⋮ Div-curl lemma with critical power weights in dimension three ⋮ Global Solutions to the Isentropic Compressible Navier--Stokes Equations with a Class of Large Initial Data ⋮ Strong solutions of the Navier-Stokes equations with singular data ⋮ Brezis-Gallouet-Wainger type inequality and its application to the Navier-Stokes equations ⋮ Unnamed Item ⋮ Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations ⋮ Unnamed Item ⋮ Les théorèmes de Leray et de Fujita-Kato pour le système de Boussinesq partiellement visqueux ⋮ Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in ℝ n ⋮ Global well-posedness of axially symmetric weak solutions to the Ginzburg–Landau model in superconductivity ⋮ GLOBAL REGULARITY TO THE NAVIER-STOKES EQUATIONS FOR A CLASS OF LARGE INITIAL DATA ⋮ The Work of Yoshihiro Shibata ⋮ Local Regularity Results for the Instationary Navier-Stokes Equations Based on Besov Space Type Criteria ⋮ Bounded Analyticity of the Stokes Semigroup on Spaces of Bounded Functions ⋮ Stability of Time Periodic Solutions for the Rotating Navier-Stokes Equations ⋮ Weighted L p − L q Estimates of Stokes Semigroup in Half-Space and Its Application to the Navier-Stokes Equations ⋮ Some remarks on the Navier–Stokes equations in R3 ⋮ Necessary and sufficient conditions on local strong solvability of the Navier–Stokes system ⋮ Real Variable Methods in Harmonic Analysis and Navier–Stokes Equations ⋮ L^p-Solutions of the Steady-State Navier–Stokes Equations with Rough External Forces ⋮ Asymptotic behavior of exact solutions for the Cauchy problem to the 3D cylindrically symmetric Navier–Stokes equations ⋮ Remarks on asymptotic behaviors of strong solutions to a viscous Boussinesq system ⋮ Navier-stokes flow in r³with measures as initial vorticity and morrey spaces ⋮ On the Behaviors of Solutions Near Possible Blow-Up Time in the Incompressible Euler and Related Equations ⋮ Optimal initial value conditions for local strong solutions of the Navier–Stokes equations in exterior domains ⋮ L p -theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle ⋮ The Role of Spectral Anisotropy in the Resolution of the Three-Dimensional Navier–Stokes Equations ⋮ On the well-posedness for the heat flow of harmonic maps and the hydrodynamic flow of nematic liquid crystals in critical spaces ⋮ Strong Solutions To The Incompressible Navier Stokes Equations In The Half Space ⋮ Uniqueness criteria for the Oseen vortex in the 3d Navier-Stokes equations ⋮ Global well-posedness of solutions for the epitaxy thin film growth model ⋮ Asymptotic behavior of the stationary magnetohydrodynamic equations in an exterior domain ⋮ Regularity and stability for the solutions of the Navier–Stokes equations in Lorentz spaces ⋮ Geometry of unbounded domains,poincaré inequalities and stability in semilinear parabolic equations

Cites Work

Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions