Relative entropy for compressible Navier-Stokes equations with density dependent viscosities and various applications

DOI10.1051/proc/201758040zbMath1387.35445OpenAlexW2962827032MaRDI QIDQ4606404

Pascal Noble, Bresch, Didier, Jean-Paul Vila

Publication date: 7 March 2018

Published in: ESAIM: Proceedings and Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/proc/201758040

zbMATH Keywords

compressible Navier-Stokes equationsinviscid limitviscous shallow water equationscompressible or incompressible Euler equationsinviscid shallow water equations

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Navier-Stokes equations (35Q30) Viscous-inviscid interaction for compressible fluids and gas dynamics (76N17) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Relative entropy for compressible Navier-Stokes equations with density-dependent viscosities and applications, Pressureless Euler with nonlocal interactions as a singular limit of degenerate Navier-Stokes system, Analysis of the generalized Aw-Rascle model, On Navier-Stokes-Korteweg and Euler-Korteweg systems: application to quantum fluids models, Inviscid limit for the compressible Navier-Stokes equations with density dependent viscosity, Global weak solutions for quantum isothermal fluids, Asymptotic analysis for a Vlasov–Fokker–Planck/Navier–Stokes system in a bounded domain, Global dissipative solutions of the defocusing isothermal Euler–Langevin–Korteweg equations

Cites Work

• Relative entropy for compressible Navier-Stokes equations with density-dependent viscosities and applications
• An accurate low-Mach scheme for a compressible two-fluid model applied to free-surface flows
• Two-velocity hydrodynamics in fluid mechanics. II. Existence of global \(\kappa\)-entropy solutions to the compressible Navier-Stokes systems with degenerate viscosities
• Some diffusive capillary models of Korteweg type
• Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity
• The second law of thermodynamics and stability
• Dissipative and entropy solutions to non-isotropic degenerate parabolic balance laws
• Relative entropies, suitable weak solutions, and weak-strong uniqueness for the compressible Navier-Stokes system
• On the inviscid limit for the compressible Navier-Stokes system in an impermeable bounded domain
• Relative entropy and hydrodynamics of Ginzburg-Landau models
• Existence of global weak solutions for 3D degenerate compressible Navier-Stokes equations
• Remarks on the inviscid limit for the compressible flows
• Existence and Uniqueness of Global Strong Solutions for One-Dimensional Compressible Navier–Stokes Equations
• Error estimates for a numerical approximation to the compressible barotropic Navier–Stokes equations
• On Some Compressible Fluid Models: Korteweg, Lubrication, and Shallow Water Systems
• On the well-posedness for the Euler-Korteweg model in several space dimensions
• Singular limits in thermodynamics of viscous fluids