Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data
From MaRDI portal
Publication:4299403
DOI10.1080/03605309408821042zbMath0803.35068OpenAlexW2027047150MaRDI QIDQ4299403
Publication date: 15 December 1994
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/03605309408821042
Nonlinear parabolic equations (35K55) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Navier-Stokes equations (35Q30) Initial value problems for second-order parabolic equations (35K15)
Related Items
Initial and boundary values for \(L_\alpha^q(L^p)\) solution of the Navier-Stokes equations in the half-space ⋮ Besov-type and Triebel-Lizorkin-type spaces associated with heat kernels ⋮ Interpolation of generalized Morrey spaces ⋮ Generalized Morrey spaces and trace operator ⋮ On analyticity rate estimates to the magneto-hydrodynamic equations in Besov-Morrey spaces ⋮ Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption ⋮ Bilinear fractional integral operators on Morrey spaces ⋮ Smoothness Morrey spaces of regular distributions, and some unboundedness property ⋮ Uniformly local \(L^p\) estimate for 2-D vorticity equations and its applications to Euler equations with initial vorticity in bmo ⋮ On the stability of global solutions to Navier--Stokes equations in the space ⋮ A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces ⋮ Strong solutions of the Navier-Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces ⋮ Optimal initial value conditions for the existence of local strong solutions of the Navier-Stokes equations ⋮ Characterization of variable Besov-type spaces by ball means of differences ⋮ Hardy inequalities and dynamic instability of singular Yamabe metrics ⋮ Morrey spaces on domains: different approaches and growth envelopes ⋮ Existence of solutions for a fractional semilinear parabolic equation with singular initial data ⋮ The incompressible limit in \(L^p\) type critical spaces ⋮ Boundedness of multidimensional Hausdorff operator on Hardy-Morrey and Besov-Morrey spaces ⋮ Dissipative quasi-geostrophic equation for large initial data in the critical Sobolev space ⋮ On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations ⋮ Uniqueness for the Navier-Stokes equations and multipliers between Sobolev spaces ⋮ A family of dissipative active scalar equations with singular velocity and measure initial data ⋮ Analyticity and existence of the Keller-Segel-Navier-Stokes equations in critical Besov spaces ⋮ Small stable stationary solutions in Morrey spaces of the Navier-Stokes equation ⋮ The Cauchy problem in local spaces for the complex Ginzburg-Landau equation. I: Compactness methods ⋮ Global solutions for the Navier-Stokes equations in the rotational framework ⋮ Existence of solutions for the 3D-micropolar fluid system with initial data in Besov-Morrey spaces ⋮ Compact embeddings of radial and subradial subspaces of some Besov-type spaces related to Morrey spaces ⋮ Stationary Navier-Stokes equations with critically singular external forces: existence and stability results ⋮ Navier-Stokes equations with external forces in Lorentz spaces and its application to the self-similar solutions ⋮ Interpolation of Morrey-Campanato and related smoothness spaces ⋮ Elliptic equations with discontinuous coefficients in generalized Morrey spaces ⋮ Musielak-Orlicz Besov-type and Triebel-Lizorkin-type spaces ⋮ On the well-posedness of the inviscid Boussinesq equations in the Besov-Morrey spaces ⋮ Decay estimate of global solutions to the generalized double dispersion model in Morrey spaces ⋮ Sobolev multipliers, maximal functions and parabolic equations with a quadratic nonlinearity ⋮ Uniform global well-posedness of the Navier-Stokes-Coriolis system in a new critical space ⋮ Time periodic solutions to the Navier-Stokes equations in the rotational framework ⋮ Parabolic fractional maximal operator in modified parabolic Morrey spaces ⋮ On a bilinear estimate in weak-Morrey spaces and uniqueness for Navier-Stokes equations ⋮ A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations ⋮ Sobolev embeddings for generalized Riesz potentials of functions in Morrey spaces \(L^{(1, \varphi)}(G)\) over nondoubling measure spaces ⋮ Spatial analyticity of solutions to the drift-diffusion equation with generalized dissipation ⋮ The Navier-Stokes equations in the critical Morrey-Campanato space ⋮ Endpoint estimates for multilinear fractional integrals with non-doubling measures ⋮ Self-similar solutions for active scalar equations in Fourier-Besov-Morrey spaces ⋮ A sharp time-weighted inequality for the compressible Navier-Stokes-Poisson system in the critical \(L^p\) framework ⋮ Solutions in mixed-norm Sobolev-Lorentz spaces to the initial value problem for the Navier-Stokes equations ⋮ On the Gagliardo-Nirenberg type inequality in the critical Sobolev-Morrey space ⋮ Existence and large time behavior to coupled chemotaxis-fluid equations in Besov-Morrey spaces ⋮ The combined quasineutral and low Mach number limit of the Navier-Stokes-Poisson system ⋮ Global well-posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey spaces ⋮ Existence and symmetries of solutions in Besov-Morrey spaces for a semilinear heat-wave type equation ⋮ Solvability of the initial-boundary value problem of the Navier-Stokes equations with rough data ⋮ A note on time-decay estimates for the compressible Navier-Stokes equations ⋮ Uniqueness results for weak Leray-Hopf solutions of the Navier-Stokes system with initial values in critical spaces ⋮ Some properties of variable Besov-type spaces ⋮ Strong summability of Fourier series and generalized Morrey spaces ⋮ Unboundedness properties of smoothness Morrey spaces of regular distributions on domains ⋮ Calderón's first and second complex interpolations of closed subspaces of Morrey spaces ⋮ Besov-weak-Herz spaces and global solutions for Navier-Stokes equations ⋮ On the heat equation with nonlinearity and singular anisotropic potential on the boundary ⋮ Optimal decay estimates in the critical \(L^{p}\) framework for flows of compressible viscous and heat-conductive gases ⋮ Global solutions to chemotaxis-Navier-Stokes equations in critical Besov spaces ⋮ Continuous embeddings of Besov-Morrey function spaces ⋮ Global well-posedness for Keller-Segel system in Besov type spaces ⋮ Local well-posedness for a Lotka-Volterra system in Besov spaces ⋮ Characterizations of Morrey type Besov and Triebel-Lizorkin spaces with variable exponents ⋮ Regularity criteria for the 3D magneto-micropolar fluid equations in the Morrey-Campanato space ⋮ Ill-posedness of the 3D-Navier-Stokes equations in a generalized Besov space near \(\mathrm{BMO}^{-1}\) ⋮ Fractional Navier-Stokes equations and a Hölder-type inequality in a sum of singular spaces ⋮ Function spaces of Besov-type and Triebel-Lizorkin-type -- a survey ⋮ Hausdorff Besov-type and Triebel-Lizorkin-type spaces and their applications ⋮ Stability properties of the regular set for the Navier-Stokes equation ⋮ Complex interpolation of Lizorkin-Triebel-Morrey spaces on domains ⋮ Global existence and Gevrey regularity to the Navier-Stokes-Nernst-Planck-Poisson system in critical Besov-Morrey spaces ⋮ Littlewood-Paley characterizations of Triebel-Lizorkin-Morrey spaces via ball averages ⋮ A critical functional framework for the inhomogeneous Navier-Stokes equations in the half-space ⋮ On the uniqueness of time-periodic solutions to the Navier-Stokes equations in unbounded domains ⋮ Asymptotic limit of fast rotation for the incompressible Navier-Stokes equations in a 3D layer ⋮ On Sobolev and Franke-Jawerth embeddings of smoothness Morrey spaces ⋮ The Keller-Segel system of parabolic-parabolic type in homogeneous Besov spaces framework ⋮ On heat convection equations in a half space with non-decaying data and Stokes semi-group on Besov spaces based on \(L^{\infty }\) ⋮ Decomposition of Hardy--Morrey spaces ⋮ Fractal Burgers equations ⋮ Maximal \(L^1\)-regularity of the heat equation and application to a free boundary problem of the Navier-Stokes equations near the half-space ⋮ Global well-posedness for the fractional Boussinesq-Coriolis system with stratification in a framework of Fourier-Besov type ⋮ Necessary and sufficient condition on initial data in the Besov space for solutions in the Serrin class of the Navier-Stokes equations ⋮ Maximal Lorentz regularity for the Keller-Segel system of parabolic-elliptic type ⋮ Well-posedness of a semilinear heat equation with weak initial data ⋮ Global mild solutions to three-dimensional magnetohydrodynamic equations in Morrey spaces ⋮ Global well-posedness, Gevrey class regularity and large time asymptotics for the dissipative quasi-geostrophic equation in Fourier-Besov spaces ⋮ New applications of Besov-type and Triebel-Lizorkin-type spaces ⋮ Some embeddings of Morrey spaces with critical smoothness ⋮ Scaling in nonlinear parabolic equations ⋮ Parabolic problems with nonlinear boundary conditions and critical nonlinearities ⋮ What is a solution to the Navier-Stokes equations? ⋮ Some specific unboundedness property in smoothness Morrey spaces. The non-existence of growth envelopes in the subcritical case ⋮ 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 ⋮ Several equivalent characterizations of fractional Hajłasz-Morrey-Sobolev spaces ⋮ Besov-Morrey spaces: Function space theory and applications to non-linear PDE ⋮ Composition operators on Herz-type Triebel-Lizorkin spaces with application to semilinear parabolic equations ⋮ L∞ estimates and integrability by compensation in Besov–Morrey spaces and applications ⋮ Well-posedness and blow-up of solutions for the 2D dissipative quasi-geostrophic equation in critical Fourier-Besov-Morrey spaces ⋮ Large-time behavior of strong solutions to the compressible magnetohydrodynamic system in the critical framework ⋮ Well-posedness for chemotaxis–fluid models in arbitrary dimensions* ⋮ Sharp estimates for homogeneous semigroups in homogeneous spaces. Applications to PDEs and fractional diffusion in ℝN ⋮ Solutions in Morrey spaces of some semilinear heat equations with time-dependent external forces ⋮ Existence of solutions to nonlinear parabolic equations via majorant integral kernel ⋮ Local and global solvability for Keller-Segel system in Besov-Morrey spaces ⋮ On the uniqueness of mild solutions for the parabolic-elliptic Keller-Segel system in the critical \(L^p \)-space ⋮ On the fractional doubly parabolic Keller-Segel system modelling chemotaxis ⋮ Global existence for an attraction-repulsion chemotaxis-fluid system in a framework of Besov-Morrey type ⋮ Time-dependent singularities in semilinear parabolic equations: existence of solutions ⋮ Complex interpolation of grand Lebesgue spaces ⋮ Global Navier-Stokes flows for non-decaying initial data with slowly decaying oscillation ⋮ Large-time behavior of solutions in the critical spaces for the non-isentropic compressible Navier-Stokes equations with capillarity ⋮ Entropy numbers of compact embeddings of smoothness Morrey spaces on bounded domains ⋮ Traces and extensions of generalized smoothness Morrey spaces on domains ⋮ Besov spaces on open sets ⋮ Morrey sequence spaces: Pitt's theorem and compact embeddings ⋮ Well-posedness for the Navier-Stokes equations in critical mixed-norm Lebesgue spaces ⋮ Complex interpolation of various subspaces of Morrey spaces ⋮ Global well-posedness of the incompressible fractional Navier-Stokes equations in Fourier-Besov spaces with variable exponents ⋮ BESOV-TYPE SPACES AND DIFFERENCES ⋮ Existence of solutions for a higher-order semilinear parabolic equation with singular initial data ⋮ ENDPOINT ESTIMATES FOR MULTILINEAR FRACTIONAL INTEGRALS ⋮ Optimal decay for the compressible Navier-Stokes equations without additional smallness assumptions ⋮ Global well-posedness for the incompressible Navier-Stokes equations in the critical Besov space under the Lagrangian coordinates ⋮ Global well-posedness for the Navier-Stokes equations with the Coriolis force in function spaces characterized by semigroups ⋮ The large-time behavior of solutions in the critical L p framework for compressible viscous and heat-conductive gas flows ⋮ Truncation in Besov-Morrey and Triebel-Lizorkin-Morrey spaces ⋮ Fujita–Kato solution for compressible Navier–Stokes equations with axisymmetric initial data and zero Mach number limit ⋮ Characterizations of weighted BMO space and its application ⋮ Decompositions of Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces ⋮ Compact embeddings of weighted smoothness spaces of Morrey type: An example ⋮ Compact embeddings in Besov-type and Triebel-Lizorkin-type spaces on bounded domains ⋮ Blow-up criterion of strong solutions to the Navier-Stokes equations in Besov spaces with negative indices ⋮ Rotating Navier-Stokes equations in \({\mathbb R}^{3}_{+}\) with initial data nondecreasing at infinity: The Ekman boundary layer problem ⋮ Weak Morrey spaces and strong solutions to the Navier-Stokes equations ⋮ Degenerate parabolic equations with initial data measures ⋮ Wavelet decomposition and embeddings of generalised Besov-Morrey spaces ⋮ Solvability of a Semilinear Heat Equation via a Quasi Scale Invariance ⋮ Parabolic equations with conservative nonlinear term and singular initial data ⋮ Local means, wavelet bases and wavelet isomorphisms in Besov‐Morrey and Triebel‐Lizorkin‐Morrey spaces ⋮ Navier–Stokes equations with external forces in Besov–Morrey spaces ⋮ Strong summability of Fourier series and Morrey spaces ⋮ Uniqueness criterion of weak solutions for the dissipative quasi-geostrophic equations in Orlicz–Morrey spaces ⋮ ON EXTENSION THEOREMS FOR ANISOTROPIC BESOV–MORREY TYPE SPACES ⋮ Global well-posedness and ill-posedness for the Navier-Stokes equations with the Coriolis force in function spaces of Besov type ⋮ The well-posedness of the surface quasi-geostrophic equations in the Besov-Morrey spaces ⋮ Self-similar solutions of the Navier-Stokes equations on weak weighted Lorentz spaces ⋮ Limiting embeddings in smoothness Morrey spaces, continuity envelopes and applications ⋮ On the local solvability in Morrey spaces of the Navier-Stokes equations in a rotating frame ⋮ Local solvability of the Keller–Segel system with Cauchy data in the Besov spaces ⋮ Existence of a forward self-similar stagnation flow of the Navier-Stokes equations ⋮ Embedding properties of Besov-type spaces ⋮ Singular integral operator, Hardy-Morrey space estimates for multilinear operators and Navier-Stokes equations ⋮ Unnamed Item ⋮ Euler equations and real harmonic analysis ⋮ Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces on domains ⋮ Pointwise and grand maximal function characterizations of Besov-type and Triebel-Lizorkin-type spaces ⋮ Global well-posedness and analyticity for the 3D fractional magnetohydrodynamics equations in variable Fourier-Besov spaces ⋮ Strong solutions of the Navier-Stokes equations with singular data ⋮ Composition estimates and well-posedness for Hardy-Hénon parabolic equations in Besov spaces ⋮ Morrey-Sobolev spaces on metric measure spaces ⋮ Characterization of initial data in the homogeneous Besov space for solutions in the Serrin class of the Navier-Stokes equations ⋮ Variable exponent Triebel-Lizorkin-Morrey spaces ⋮ Variable exponent Besov-Morrey spaces ⋮ Well-posedness of the Euler equation in Triebel–Lizorkin–Morrey spaces ⋮ Navier-stokes equations on unbounded domains with rough initial data ⋮ Some quantitative result on compact embeddings in smoothness Morrey spaces on bounded domains; an approach via interpolation ⋮ Interpolation, extrapolation, Morrey spaces and local energy control for the Navier–Stokes equations ⋮ Some remarks on the Navier–Stokes equations in R3 ⋮ Existence and asymptotic behavior to the incompressible nematic liquid crystal flow in the whole space ⋮ Bilinear estimates and uniqueness for Navier-Stokes equations in critical Besov-type spaces ⋮ Decomposition for Morrey type Besov-Triebel spaces ⋮ Non-smooth decomposition of homogeneous Triebel−Lizorkin−Morrey spaces ⋮ Real Variable Methods in Harmonic Analysis and Navier–Stokes Equations ⋮ Existence and large time behavior to the nematic liquid crystal equations in Besov-Morrey spaces ⋮ Global well-posedness and asymptotic behavior in Besov-Morrey spaces for chemotaxis-Navier-Stokes fluids ⋮ Solvability of a Semilinear Parabolic Equation with Measures as Initial Data ⋮ Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity ⋮ Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces for nondoubling measures ⋮ Coifman–Meyer multipliers: Leibniz-type rules and applications to scattering of solutions to PDEs ⋮ On the existence and uniqueness of mild and strong solutions of a generalized nonlinear heat equation ⋮ On the fractional chemotaxis Navier-Stokes system in the critical spaces ⋮ A low-frequency assumption for optimal time-decay estimates to the compressible Navier-Stokes equations ⋮ On the equivalence of the \(K\)-functional and the modulus of continuity on the Morrey spaces ⋮ Uniqueness criteria for the Oseen vortex in the 3d Navier-Stokes equations ⋮ Fractional Hajłasz–Morrey–Sobolev spaces on quasi-metric measure spaces ⋮ COMPLEX INTERPOLATION ON BESOV-TYPE AND TRIEBEL–LIZORKIN-TYPE SPACES ⋮ Solvability of superlinear fractional parabolic equations ⋮ Regularity and stability for the solutions of the Navier–Stokes equations in Lorentz spaces ⋮ Global solutions for the critical Burgers equation in the Besov spaces and the large time behavior ⋮ On existence and scattering theory for the Klein-Gordon-Schrödinger system in an infinite \(L^{2}\)-norm setting ⋮ Time periodic solutions to the 2D quasi-geostrophic equation with the supercritical dissipation ⋮ Embeddings of weighted Morrey spaces ⋮ Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces ⋮ Solvability of a semilinear heat equation on Riemannian manifolds ⋮ Limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces on domains and an extension operator ⋮ Adams’ trace principle in Morrey–Lorentz spaces on β-Hausdorff dimensional surfaces ⋮ Maximal regularity of the heat evolution equation on spatial local spaces and application to a singular limit problem of the Keller-Segel system ⋮ Vortex Filament Solutions of the Navier‐Stokes Equations ⋮ 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 ⋮ Existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces ⋮ An application of BMO-type space to chemotaxis-fluid equations ⋮ Fractional Leibniz rules in the setting of quasi-Banach function spaces ⋮ Singular limit problem for the Keller-Segel system and drift-diffusion system in scaling critical Besov-Morrey spaces ⋮ On linear higher-order parabolic equations in Morrey spaces ⋮ Well‐posedness and asymptotic behavior for the fractional Keller–Segel system in critical Besov–Herz‐type spaces ⋮ On the stability to Keller-Segel system coupled with Navier-Stokes equations in Besov-Morrey spaces ⋮ Semilinear parabolic equations in Herz spaces ⋮ Navier-Stokes equation with hereditary viscosity and initial data in Besov-Morrey spaces ⋮ Initial traces and solvability for a semilinear heat equation on a half space of ℝ^{ℕ} ⋮ The Leibniz rule for the Dirichlet and the Neumann Laplacian ⋮ Forces for the Navier-Stokes equations and the Koch and Tataru theorem ⋮ Characterizations of the BMO and Lipschitz spaces via commutators on weak Lebesgue and Morrey spaces ⋮ Generalized Besov-type and Triebel–Lizorkin-type spaces ⋮ Gevrey class regularity and stability for the Debye-H¨uckel system in critical Fourier-Besov-Morrey spaces ⋮ Unnamed Item ⋮ Preface ⋮ Embedding properties of weighted Besov-type spaces ⋮ Asymptotic stability of stationary Navier–Stokes flow in Besov spaces
Cites Work
- Unnamed Item
- Unnamed Item
- Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
- Theory of function spaces
- Two-dimensional Navier-Stokes flow with measures as initial vorticity
- Existence and non-existence of global solutions for a semilinear heat equation
- Navier and Stokes meet the wavelet
- Remarks on Navier-Stokes equations with measures as data
- On the theory of \({\mathcal L}_{p, \lambda}\) spaces
- Problems paraboliques semi-lineaires avec donnees measures
- Abstract Besov space approach to the non-stationary Navier-Stokes equations
- Analysis on Morrey Spaces and Applications to Navier-Stokes and Other Evolution Equations
- Navier-stokes flow in r3with measures as initial vorticity and morrey spaces
- On nonexistence of global solutions of some semilinear parabolic differential equations
- Strong solutions of the Navier-Stokes equation in Morrey spaces