Relative entropies, suitable weak solutions, and weak strong uniqueness for the compressible Navier-Stokes system

Abstract

We introduce the notion of relative entropy for the weak solutions of the compressible Navier-Stokes system. We show that any finite energy weak solution satisfies a relative entropy inequality for any pair of sufficiently smooth test functions. As a corollary we establish weak-strong uniqueness principle for the compressible Navier-Stokes system.

Cited by in corpus (56)

• Weak-strong uniqueness property for the full Navier-Stokes-Fourier system
• Well/ill posedness for the Euler-Korteweg-Poisson system and related problems
• Weak-strong uniqueness for measure-valued solutions of some compressible fluid models
• On the inviscid limit for the compressible Navier-Stokes system in an impermeable bounded domain
• Thermodynamics and stability of non-equilibrium steady states in open systems
• Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension
• Uniqueness of solutions for a mathematical model for magneto-viscoelastic flows
• Weak-strong uniqueness for measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen-Frank free energy
• On the motion of viscous, compressible and heat-conducting liquids
• On a class of compressible viscoelastic rate-type fluids with stress--diffusion
• On the vanishing electron-mass limit in plasma hydrodynamics in unbounded media
• Dimension reduction for the full Navier-Stokes-Fourier system
• Existence, regularity and weak-strong uniqueness for the three-dimensional Peterlin viscoelastic model
• On weak solutions to the problem of a rigid body with a cavity filled with a compressible fluid, and their asymptotic behavior
• Low stratification of a heat-conducting fluid in time-dependent domain
• Asymptotic analysis for Vlasov-Fokker-Planck/compressible Navier-Stokes equations with a density-dependent viscosity
• Vanishing viscosity limit for the compressible Navier-Stokes system via measure-valued solutions
• Derivation of the Navier - Stokes - Poisson system with radiation for an accretion disk
• Existence of dissipative solutions to the compressible Navier-Stokes system with potential temperature transport
• Dissipative measure-valued solutions to the compressible Navier-Stokes system
• Weak-strong uniqueness for the general Ericksen-Leslie system in three dimensions
• On weak-strong uniqueness for compressible Navier-Stokes system with general pressure laws
• Low Mach number limit on thin domains
• Weak-strong uniqueness property for models of compressible viscous fluids near vacuum
• Weak-strong uniqueness for the Navier-Stokes equation for two fluids with ninety degree contact angle and same viscosities
• A posteriori analysis for dynamic model adaptation in convection dominated problems
• Rigorous derivation and well-posedness of a quasi-homogeneous ideal MHD system
• Numerical analysis of a model of two phase compressible fluid flow
• On Navier-Stokes-Korteweg and Euler-Korteweg Systems: Application to Quantum Fluids Models
• On weak (measure-valued)-strong uniqueness for compressible Navier-Stokes system with non-monotone pressure law
• A note on the uniqueness of weak solutions to a class of cross-diffusion systems
• A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness
• On convergence of numerical solutions for the compressible MHD system with exactly divergence-free magnetic field
• On weak-strong uniqueness property for the full compressible magnetohydrodynamics flows
• Analytical solution of the incompressible Navier-Stokes equations
• On a singular limit for the compressible rotating Euler system
• Flow of heat conducting fluid in a time dependent domain
• Weak-strong uniqueness of solutions to entropy-dissipating reaction-diffusion equations
• Dimension reduction for the compressible Navier-Stokes system with density dependent viscosity
• Low Mach and thin domain limit for the compressible Euler system
• Relative entropy, weak-strong uniqueness and conditional regularity for a compressible Oldroyd-B model
• Convergence and error estimates for a finite difference scheme for the multi-dimensional compressible Navier-Stokes system
• Scale interactions in compressible rotating fluids
• On weak solutions to the 2D Savage-Hutter model of the motion of a gravity driven avalanche flow
• Robustness of strong solutions to the compressible Navier-Stokes system
• On singular limits arising in the scale analysis of stratified fluid flows
• Remarks on weak-strong uniqueness for two-fluid model
• Multiple scales and singular limits for compressible rotating fluids with general initial data
• Weak-strong uniqueness for compressible Navier-Stokes system with slip boundary conditions on time dependent domains
• On weak-strong uniqueness and singular limit for the compressible Primitive Equations
• Singular limit for the compressible Navier--Stokes equations with the hard sphere pressure law on expanding domains
• Low Mach Number Limit of a Diffuse Interface Model for Two-Phase Flows of Compressible Viscous Fluids
• Weak solutions and singular limits for a compressible fluid-structure interaction problem with slip boundary conditions
• Mv-strong uniqueness for density dependent, non-Newtonian, incompressible fluids
• On weak-strong uniqueness for the compressible Navier-Stokes system with non-monotone pressure law
• Existence and stability of dissipative turbulent solutions to a simple bi-fluid model of compressible fluids