Le problème de Cauchy pour les équations différentielles d'un fluide général
From MaRDI portal
Publication:5719874
DOI10.24033/bsmf.1586zbMath0113.19405OpenAlexW1868633469WikidataQ110828919 ScholiaQ110828919MaRDI QIDQ5719874
Publication date: 1962
Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=BSMF_1962__90__487_0
Related Items
Compressible Navier-Stokes equations with revised Maxwell's law ⋮ On classical solutions to 2D shallow water equations with degenerate viscosities ⋮ Emergence of a Hierarchy of Singularities in Zero-Pressure Media. Two-Dimensional Case ⋮ Global strong solutions to planar radiative magnetohydrodynamic equations with density-dependent viscosity and degenerate heat-conductivity ⋮ The stability of contact discontinuity for the planar thermally radiative magnetohydrodynamics with free boundary ⋮ Local Strong Solutions to the Full Compressible Navier--Stokes System with Temperature-Dependent Viscosity and Heat Conductivity ⋮ Well-posedness and exponential decay for the Navier–Stokes equations of viscous compressible heat-conductive fluids with vacuum ⋮ Local weak solution of the isentropic compressible Navier-Stokes equations in a half-space ⋮ Ill-posedness for the compressible Navier-Stokes equations under barotropic condition in limiting Besov spaces ⋮ Global solutions of the Navier-Stokes equations for isentropic flow with large external potential force ⋮ On blowup of classical solutions to the compressible Navier-Stokes equations ⋮ Global large solutions and incompressible limit for the compressible Navier-Stokes equations ⋮ Global strong solutions to 1-D vacuum free boundary problem for compressible Navier-Stokes equations with variable viscosity and thermal conductivity ⋮ Global well-posedness of the Cauchy problem of two-dimensional compressible Navier-Stokes equations in weighted spaces ⋮ Classical solutions of the 3D compressible fluid-particle system with a magnetic field ⋮ On the Cauchy problem of 3D compressible, viscous, heat-conductive Navier-Stokes-Poisson equations subject to large and non-flat doping profile ⋮ Global existence of strong and weak solutions to 2D compressible Navier-Stokes system in bounded domains with large data and vacuum ⋮ Global well-posedness of compressible Navier-Stokes equation with \(BV\cap L^1\) initial data ⋮ Unnamed Item ⋮ On global strong solutions to the 3D MHD flows with density-temperature-dependent viscosities ⋮ A numerical approach for the existence of dissipative weak solutions to a compressible two-fluid model ⋮ The global existence of strong solutions to the 3D compressible isothermal Navier-Stokes equations ⋮ Global solutions to a 3D axisymmetric compressible Navier-Stokes system with density-dependent viscosity ⋮ Global Stabilization of Compressible Flow between Two Moving Pistons ⋮ Global well-posedness for the full compressible Navier-Stokes equations ⋮ On the Cauchy problem of the full Navier-Stokes equations for three-dimensional compressible viscous heat-conducting flows subject to large external potential forces ⋮ Unnamed Item ⋮ Global solution to the compressible non-isothermal nematic liquid crystal equations with constant heat conductivity and vacuum ⋮ Global Well-Posedness of Classical Solutions to the Cauchy Problem of Two-Dimensional Barotropic Compressible Navier--Stokes System with Vacuum and Large Initial Data ⋮ On the implosion of a compressible fluid. II: Singularity formation ⋮ On free boundary problem for compressible Navier-Stokes equations with temperature-dependent heat conductivity ⋮ Hyperbolic compressible Navier-Stokes equations ⋮ Global small solutions of heat conductive compressible Navier-Stokes equations with vacuum: smallness on scaling invariant quantity ⋮ Global classical solutions to the 2D compressible Navier-Stokes equations with vacuum ⋮ Long-time behavior for three dimensional compressible viscousand heat-conductive gases ⋮ On regular solutions to compressible radiation hydrodynamic equations with far field vacuum ⋮ Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations ⋮ The Cauchy Problem for the \(\boldsymbol{N}\)-Dimensional Compressible Navier–Stokes Equations without Heat Conductivity ⋮ Immediate Blowup of Entropy-Bounded Classical Solutions to the Vacuum Free Boundary Problem of Nonisentropic Compressible Navier–Stokes Equations ⋮ Global Regular Solutions for one-dimensional Degenerate Compressible Navier--Stokes Equations with Large Data and Far Field Vacuum ⋮ Blow up criteria for the 2D compressible Navier-Stokes equations in bounded domains with vacuum ⋮ Global Large Solutions to the Three Dimensional Compressible Navier--Stokes Equations ⋮ Global large solutions to planar magnetohydrodynamics equations with temperature-dependent coefficients ⋮ Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data ⋮ Vanishing viscosity limit of the three-dimensional barotropic compressible Navier-Stokes equations with degenerate viscosities and far-field vacuum ⋮ Stability of stationary solutions for inflow problem on the planar magnetohydrodynamics ⋮ Global well-posedness and exponential decay rates of the strong solutions to the two-dimensional full compressible magnetohydrodynamics equations with vacuum in some class of large initial data ⋮ Global existence and decay of strong solutions to the compressible Navier-Stokes-Poisson equations in bounded domains ⋮ Local existence of strong solutions of a fluid-structure interaction model ⋮ Singularity formation of the compressible non-barotropic flows with zero heat conductivity ⋮ Regularity and uniqueness for the compressible full Navier-Stokes equations ⋮ Optimal decay for the compressible Navier-Stokes equations without additional smallness assumptions ⋮ The unique global solvability and optimal time decay rates for a multi-dimensional compressible generic two-fluid model with capillarity effects * ⋮ Boundary value problems for equations of viscous heat-conducting gas in time-increasing non-cylindrical domains ⋮ Weak solutions of the Navier-Stokes equations for compressible flows in a half-space with no-slip boundary conditions ⋮ Global well-posedness of compressible Navier-Stokes equations for some classes of large initial data ⋮ Weak Serrin‐type criterion for the three‐dimensional viscous compressible Navier–Stokes system ⋮ Large time behavior for a compressible two-fluid model with algebraic pressure closure and large initial data ⋮ Decay of strong solution for the compressible Navier-Stokes equations with large initial data ⋮ Global existence of strong solutions to MHD with density-depending viscosity and temperature-depending heat-conductivity in unbounded domains ⋮ On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum ⋮ On one-dimensional compressible Navier-Stokes equations with degenerate viscosity and constant state at far fields ⋮ Global well-posedness of 2D compressible Navier-Stokes equations with large data and vacuum ⋮ LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES ⋮ Global well-posedness and large time asymptotic behavior of classical solutions to the compressible Navier-Stokes equations with vacuum ⋮ Système d'équations d'un gaz visqueux modélisant l'atmosphère avec la force de Coriolis et la stabilité de l'état d'équilibre ⋮ On global solutions and asymptotic behavior of planar magnetohydrodynamics with large data ⋮ Global Solutions to the Isentropic Compressible Navier--Stokes Equations with a Class of Large Initial Data ⋮ On initial boundary value problems for planar magnetohydrodynamics with large data ⋮ The local existence and blowup criterion for strong solutions to the kinetic Cucker-Smale model coupled with the compressible Navier-Stokes equations ⋮ One new blowup criterion for the 2D full compressible Navier-Stokes system ⋮ Asymptotic behavior of global smooth solutions for full compressible Navier-Stokes-Maxwell equations ⋮ On a simplified compressible Navier-Stokes equations with temperature-dependent viscosity ⋮ Nonlinearly exponential stability of compressible Navier-Stokes system with degenerate heat-conductivity ⋮ Entropy bounded solutions to the one-dimensional compressible Navier-Stokes equations with zero heat conduction and far field vacuum ⋮ A well-posedness result for viscous compressible fluids with only bounded density ⋮ Vanishing shear viscosity limit and boundary layer study for the planar MHD system ⋮ Convergence to equilibrium for the solution of the full compressible Navier-Stokes equations ⋮ Existence and uniqueness of small energy weak solution to multi-dimensional compressible Navier-Stokes equations with large external potential force ⋮ Global strong solutions to the 3D full compressible Navier-Stokes equations with density-temperature-dependent viscosities in bounded domains ⋮ The large time behavior of the free boundary for one dimensional compressible Navier-Stokes equations ⋮ Global strong solutions to magnetohydrodynamics with density-dependent viscosity and degenerate heat-conductivity ⋮ Global strong solutions to the two-dimensional full compressible Navier-Stokes equations with vacuum ⋮ ILL-POSEDNESS FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH THE VELOCITY IN FRAMEWORK ⋮ Global stability of large solutions to the 3D compressible Navier-Stokes equations ⋮ On classical solutions for viscous polytropic fluids with degenerate viscosities and vacuum ⋮ Converge rates towards stationary solutions for the outflow problem of planar magnetohydrodynamics on a half line ⋮ A Serrin criterion for compressible nematic liquid crystal flows ⋮ A low-frequency assumption for optimal time-decay estimates to the compressible Navier-Stokes equations ⋮ Global weak solutions for the Cauchy problem to one-dimensional heat-conductive MHD equations of viscous non-resistive gas ⋮ Global strong solutions for viscous radiative gas with degenerate temperature dependent heat conductivity in one-dimensional unbounded domains ⋮ Local weak solution of the isentropic compressible Navier–Stokes equations ⋮ Existence results for viscous polytropic fluids with degenerate viscosity coefficients and vacuum ⋮ Global solutions of compressible barotropic Navier–Stokes equations with a density-dependent viscosity coefficient ⋮ On the Global Motion of Viscous Compressible Barotropic Flows Subject to Large External Potential Forces and Vacuum ⋮ Global well-posedness of non-heat conductive compressible Navier–Stokes equations in 1D ⋮ Remark on stability of rarefaction waves to the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefficient ⋮ Global regularity to the two dimensional compressible Navier-Stokes equations with mass diffusion ⋮ Global large solutions of magnetohydrodynamics with temperature-dependent heat conductivity ⋮ Global solutions of nonlinear magnetohydrodynamics with large initial data ⋮ On the one-dimensional motion of the polytropic ideal gas non-fixed on the boundary ⋮ The solvability of the initial boundary-value problem for equations of motion of a viscous compressible barotropic liquid in the spaces \(W_ 2^{2+\ell,1+\ell/2}(Q_ T)\) ⋮ An existence theorem for compressible viscous fluids ⋮ Refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure ⋮ The equation of potential flows of a compressible viscous fluid at small Reynolds numbers: Existence, uniqueness, and stabilization of solutions ⋮ Existence and blowup behavior of global strong solutions to the two-dimensional barotropic compressible Navier-Stokes system with vacuum and large initial data ⋮ Navier-Stokes equations for compressible fluids: Global existence and qualitative properties of the solutions in the general case ⋮ Global well-posedness of strong solutions to the two-dimensional barotropic compressible Navier-Stokes equations with vacuum ⋮ Existence of global solutions for 2-dimensional viscous compressible flows ⋮ Global classical solutions of compressible isentropic Navier-Stokes equations with small density ⋮ Blowup analysis for two-dimensional viscous compressible, heat-conductive Navier-Stokes equations ⋮ Existence results for viscous polytropic fluids with vacuum ⋮ Existence and uniqueness for viscous steady compressible motions ⋮ A Nobel prize for John Nash ⋮ The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball. II: 3D Navier-Stokes equations ⋮ Weak-strong uniqueness for the isentropic compressible Navier-Stokes system ⋮ Global regularity of solution for general degenerate parabolic equations in 1-D ⋮ Well-posedness in critical spaces for a multi-dimensional compressible viscous liquid-gas two-phase flow model ⋮ Existence of a global solution for a viscoelastic system ⋮ Serrin-type blowup criterion for viscous, compressible, and heat conducting Navier-Stokes and magnetohydrodynamic flows ⋮ Dispersive effects of weakly compressible and fast rotating inviscid fluids ⋮ Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities ⋮ Global solution to 3D spherically symmetric compressible Navier-Stokes equations with large data ⋮ Cauchy problem for the equation of gasdynamics with viscosity ⋮ Global existence of weak solution to the free boundary problem for compressible Navier-Stokes ⋮ A Beale-Kato-Majda blow-up criterion for the 3-D compressible Navier-Stokes equations ⋮ Blowup criterion for viscous baratropic flows with vacuum states ⋮ Blow up of classical solutions to the isentropic compressible Navier-Stokes equations ⋮ Blowup criteria for strong solutions to the compressible Navier-Stokes equations with variable viscosity ⋮ Solvability of the initial-boundary-value problem for the equations of motion of a viscous compressible fluid ⋮ Existence of strong solutions in critical spaces for barotropic viscous fluids in larger spaces ⋮ Serrin-type blowup criterion for full compressible Navier-Stokes system ⋮ Large-time behavior of solutions to the equations of a viscous heat-conducting flow with shear viscosity in unbounded domains ⋮ Global classical and weak solutions to the three-dimensional full compressible Navier-Stokes system with vacuum and large oscillations ⋮ Well-posedness in critical spaces for the system of compressible Navier-Stokes in larger spaces ⋮ On the initial boundary-value problem for viscous heat conducting compressible fluids ⋮ On the initial-value problem for compressible fluid flows with vanishing viscosity ⋮ A combustion problem in cylindrical and spherical symmetry ⋮ Existence and continuous dependence for solutions to the equations of a one-dimensional model in gas-dynamics ⋮ Unique solvability of the initial boundary value problems for compressible viscous fluids. ⋮ From compressible to incompressible inhomogeneous flows in the case of large data ⋮ Stability of planar rarefaction wave to 3D full compressible Navier-Stokes equations ⋮ Existence and uniqueness of global classical solutions to 3D isentropic compressible Navier-Stokes equations with general initial data ⋮ Classical and quantum mechanical models of many-particle systems. Abstracts from the workshop held December 3--9, 2017 ⋮ Non-existence of classical solutions with finite energy to the Cauchy problem of the compressible Navier-Stokes equations ⋮ On the global existence of classical solutions for compressible Navier-Stokes equations with vacuum ⋮ Global existence of classical solutions for isentropic compressible Navier-Stokes equations with small initial density ⋮ Blow-up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations ⋮ Global strong solution to compressible Navier-Stokes equations with density dependent viscosity and temperature dependent heat conductivity ⋮ Global well-posedness to the one-dimensional model for planar non-resistive magnetohydrodynamics with large data and vacuum ⋮ Stability of steady-state solutions to Navier-Stokes-Poisson systems ⋮ Global classical solution to two-dimensional compressible Navier-Stokes equations with large data in \(\mathbb{R}^2\) ⋮ The stability of contact discontinuity for compressible planar magnetohydrodynamics ⋮ On center singularity for compressible spherically symmetric nematic liquid crystal flows ⋮ Stability of composite wave for inflow problem on the planar magnetohydrodynamics ⋮ Global strong solution for the full MHD equations with vacuum and large data ⋮ Global existence of large solutions to the planar magnetohydrodynamic equations with zero magnetic diffusivity ⋮ Mass concentration phenomenon to the 2D Cauchy problem of the compressible Navier-Stokes equations ⋮ On the Navier-Stokes equations for three-dimensional compressible barotropic flow subject to large external potential forces with discontinuous initial data ⋮ A blow-up criterion of strong solutions to the 2D compressible Navier-Stokes equations ⋮ On scaling invariance and type-I singularities for the compressible Navier-Stokes equations ⋮ Global strong solutions for a class of heat-conducting non-Newtonian fluids with vacuum ⋮ Dynamical stability of non-constant equilibria for the compressible Navier-Stokes equations in Eulerian coordinates ⋮ On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces ⋮ Existence of global strong solutions in critical spaces for barotropic viscous fluids ⋮ Global strong solution for compressible and radiative MHD flow with density-dependent viscosity and degenerate heat-conductivity in unbounded domains ⋮ Global strong solutions to the one-dimensional heat-conductive model for planar non-resistive magnetohydrodynamics with large data ⋮ On formation of singularity for full compressible Navier-Stokes system with zero heat conduction ⋮ On the breakdown of regular solutions with finite energy for 3D degenerate compressible Navier-Stokes equations ⋮ On the first initial-boundary value problem of compressible viscous fluid motion ⋮ On the compressible Navier-Stokes equations in the whole space: from non-isentropic flow to isentropic flow ⋮ Global weak solution to 3D compressible flows with density-dependent viscosity and free boundary ⋮ Existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions ⋮ Existence and uniqueness of weak solutions of the compressible spherically symmetric Navier-Stokes equations ⋮ Strong solution to the compressible magnetohydrodynamic equations with vacuum ⋮ On local classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations with vacuum ⋮ Existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force ⋮ Well-posedness of the three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities and far field vacuum ⋮ Decay estimates of solutions to the compressible micropolar fluids system in \(\mathbb{R}^3\) ⋮ Global well-posedness of regular solutions to the three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities and vacuum ⋮ Ill-posedness for the Cauchy problem of the two-dimensional compressible Navier-Stokes equations for an ideal gas ⋮ Global large solutions to the Cauchy problem of planar magnetohydrodynamics equations with temperature-dependent coefficients ⋮ Global strong solution to the two-dimensional full compressible Navier-Stokes equations with large viscosity ⋮ Steady compressible Navier-Stokes-Fourier equations with Dirichlet boundary condition for the temperature ⋮ Existence of global strong solutions for a reduced gravity two-and-a-half layer model ⋮ Global existence of classical solutions for two-dimensional isentropic compressible Navier-Stokes equations with small initial mass ⋮ Optimal decay rates of isentropic compressible Navier-Stokes equations with discontinuous initial data ⋮ Asymptotic behavior of the solution to the system for a viscous reactive gas ⋮ Local-in-time existence of strong solutions to a class of the compressible non-Newtonian Navier-Stokes equations ⋮ Optimal decay of compressible Navier-Stokes equations with or without potential force ⋮ Existence theorems for compressible viscous fluids having zero shear viscosity ⋮ Global existence of weak solution for the compressible Navier-Stokes-Poisson system with density-dependent viscosity ⋮ Global large solutions to the planar magnetohydrodynamics equations with constant heat conductivity ⋮ Local existence and uniqueness of heat conductive compressible Navier-Stokes equations in the presence of vacuum without initial compatibility conditions ⋮ On regular solutions for three-dimensional full compressible Navier-Stokes equations with degenerate viscosities and far field vacuum ⋮ Global solutions of the Navier-Stokes equations for viscous compressible flows. ⋮ The optimal decay rate of strong solution for the compressible Navier-Stokes equations with large initial data ⋮ The strong inviscid limit of the isentropic compressible Navier-Stokes equations with Navier boundary conditions ⋮ On formation of singularity for non-isentropic Navier-Stokes equations without heat-conductivity ⋮ Large global solutions of the compressible Navier-Stokes equations in three dimensions ⋮ Global Existence Versus Blow-Up for Multidimensional Hyperbolized Compressible Navier–Stokes Equations ⋮ Local and global well-posedness of entropy-bounded solutions to the compressible Navier-Stokes equations in multi-dimensions ⋮ Critical regularity issues for the compressible Navier-Stokes system in bounded domains ⋮ The existence results for a new 2‐D compressible fluid model with the horizontal thermal gradient effect ⋮ Global classical solutions to the compressible Navier–Stokes equations with Navier-type slip boundary condition in 2D bounded domains ⋮ Global strong solutions of 3D compressible isothermal magnetohydrodynamics ⋮ Global strong solutions of 3D compressible Navier-Stokes equations with short pulse type initial data ⋮ Global solutions of \(2D\) isentropic compressible Navier-Stokes equations with one slow variable ⋮ The initial value problem for the equations of motion of fractional compressible viscous fluids ⋮ The regularity and uniqueness of a global solution to the isentropic Navier-Stokes equation with rough initial data ⋮ Propagation of Rough Initial Data for Navier–Stokes Equation ⋮ Decay of the compressible Navier-Stokes equations with hyperbolic heat conduction ⋮ A particle method for 1‐D compressible fluid flow ⋮ Global solutions of 3D isentropic compressible Navier-Stokes equations with two slow variables ⋮ On some types of initial-boundary value problems for the compressible Navier-Stokes equations with temperature-dependent and degenerate heat conductivity ⋮ Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment ⋮ Some Serrin type blow‐up criteria for the three‐dimensional viscous compressible flows with large external potential force ⋮ On the vanishing elastic limit of compressible liquid crystal material flow ⋮ On the regularity criteria for the three‐dimensional compressible Navier–Stokes system in Lorentz spaces ⋮ Global existence of strong solutions to the 3D isentropic compressible Navier–Stokes equations with density‐dependent viscosities ⋮ Extension of the Hoff solutions framework to cover Navier-Stokes equations for a compressible fluid with anisotropic viscous-stress tensor ⋮ Existence and exponential growth of global classical solutions to the compressible Navier-Stokes equations with slip boundary conditions in 3D bounded domains ⋮ On initial boundary value problems for the compressible Navier-Stokes system with temperature dependent heat conductivity ⋮ Blow-up criteria for a fluid dynamical model arising in astrophysics ⋮ Global existence for a class of large solution to compressible Navier-Stokes equations with vacuum
Cites Work
This page was built for publication: Le problème de Cauchy pour les équations différentielles d'un fluide général
