Local and global well-posedness of entropy-bounded solutions to the compressible Navier-Stokes equations in multi-dimensions

DOI10.1007/s11425-022-2047-0zbMath1525.35193MaRDI QIDQ6051320

Jinkai Li, Zhouping Xin

Publication date: 19 October 2023

Published in: Science China. Mathematics (Search for Journal in Brave)

zbMATH Keywords

strong solutionsfar field vacuuminhomogeneous Sobolev spacesuniform boundedness of entropyheat conductive compressible Navier-Stokes equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Gas dynamics (general theory) (76N15) Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35) Diffusive and convective heat and mass transfer, heat flow (80A19)

Related Items (1)

Local existence and uniqueness of heat conductive compressible Navier-Stokes equations in the presence of vacuum without initial compatibility conditions

Cites Work

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• Some uniform estimates and large-time behavior of solutions to one-dimensional compressible Navier-Stokes system in unbounded domains with large data
• On the uniqueness of compressible fluid motions
• Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids
• Existence results for viscous polytropic fluids with vacuum
• Axisymmetric solutions of the 3D Navier-Stokes equations for compressible isentropic fluids
• Cauchy problem for viscous gas equations
• An existence theorem for compressible viscous fluids
• Navier-Stokes equations for compressible fluids: Global existence and qualitative properties of the solutions in the general case
• The initial value problem for the equations of motion of viscous and heat-conductive gases
• Decay estimates for the compressible Navier-Stokes equations in unbounded domains
• On the first initial-boundary value problem of compressible viscous fluid motion
• Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas
• Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases
• Decay estimates of solutions for the equations of motion of compressible viscous and heat-conductive gases in an exterior domain in \(\mathbb{R}^3\)
• Discontinuous solutions of the Navier-Stokes equations for multidimensional flows of heat-conducting fluids
• On stability of generalized solutions to the equations of one-dimensional motion of a viscous heat conducting gas
• Unique solvability of the initial boundary value problems for compressible viscous fluids.
• Global existence of weak solutions for compressible Navier-Stokes equations: thermodynamically unstable pressure and anisotropic viscous stress tensor
• Global classical and weak solutions to the three-dimensional full compressible Navier-Stokes system with vacuum and large oscillations
• Non-existence of classical solutions with finite energy to the Cauchy problem of the compressible Navier-Stokes equations
• Optimal decay estimates in the critical \(L^{p}\) framework for flows of compressible viscous and heat-conductive gases
• On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces
• Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum
• Local existence and uniqueness of heat conductive compressible Navier-Stokes equations in the presence of vacuum without initial compatibility conditions
• Global small solutions of heat conductive compressible Navier-Stokes equations with vacuum: smallness on scaling invariant quantity
• On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum
• Global well-posedness and large time asymptotic behavior of classical solutions to the compressible Navier-Stokes equations with vacuum
• Entropy bounded solutions to the one-dimensional compressible Navier-Stokes equations with zero heat conduction and far field vacuum
• On blowup of classical solutions to the compressible Navier-Stokes equations
• On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities
• Global Solutions to the Three-Dimensional Full Compressible Navier--Stokes Equations with Vacuum at Infinity in Some Classes of Large Data
• Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations
• Global well-posedness for compressible Navier-Stokes equations with highly oscillating initial velocity
• An existence theorem for compressible viscous and heat conducting fluids
• Global existence of small solutions to a class of nonlinear evolution equations
• Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density
• Global solutions of the compressible navier-stokes equations with larger discontinuous initial data
• Global well-posedness of the Cauchy problem for the equations of a one-dimensional viscous heat-conducting gas with Lebesgue initial data
• Global Solutions to the Isentropic Compressible Navier--Stokes Equations with a Class of Large Initial Data
• Global well-posedness of non-heat conductive compressible Navier–Stokes equations in 1D
• Global Well-Posedness of the One-Dimensional Compressible Navier--Stokes Equations with Constant Heat Conductivity and Nonnegative Density
• On the Cauchy problem for the system of fundamental equations describing the movement of compressible viscous fluid
• ON THE CAUCHY PROBLEM FOR COMPOSITE SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS
• Le problème de Cauchy pour les équations différentielles d'un fluide général
• Entropy‐Bounded Solutions to the One‐Dimensional Heat Conductive Compressible Navier‐Stokes Equations with Far Field Vacuum
• Non-formation of vacuum states for compressible Navier-Stokes equations
• Global existence in critical spaces for flows of compressible viscous and heat-conductive gases
• On the existence of globally defined weak solutions to the Navier-Stokes equations

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