Uniqueness and stability of entropy shocks to the isentropic Euler system in a class of inviscid limits from a large family of Navier–Stokes systems

2020/10/15 by Moon-Jin Kang, Alexis F. Vasseur, Alexis Vasseur · 39 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Classical mechanics #Computational Fluid Dynamics and Aerodynamics #Entropy (arrow of time) #Euler equations #Euler system #Inviscid flow #Isentropic process #Mathematical analysis #Mathematics #Mechanics #Navier-Stokes equation solutions #Physics #Thermodynamics #Uniqueness #Viscosity

paper · doi:10.1007/s00222-020-01004-2

published in Inventiones mathematicae 224(1), 55-146 (Springer Science+Business Media)

openalex publication_date 2020/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Citations

• The second law of thermodynamics and stability
• Relative Entropy and the Stability of Shocks and Contact Discontinuities for Systems of Conservation Laws with non-BV Perturbations
• Criteria on Contractions for Entropic Discontinuities of Systems of Conservation Laws

Cited by

• Well-posedness of the Riemann problem with two shocks for the isentropic Euler system in a class of vanishing physical viscosity limits
• Long-time behavior towards viscous-dispersive shock for Navier-Stokes equations of Korteweg type
• Time-asymptotic stability of composite waves of viscous shock and rarefaction for barotropic Navier-Stokes equations
• Asymptotic behavior toward viscous shock for impermeable wall and inflow problem of barotropic Navier-Stokes equations
• Asymptotic stability of planar viscous shock wave to three-dimensional relaxed compressible Navier-Stokes equations
• Stability of viscous shock for the Navier-Stokes-Fourier system: outflow and impermeable wall problems
• Asymptotic stability of composite waves of shock profile and rarefaction for the Navier-Stokes-Poisson system
• Stability of Large-Amplitude Viscous Shock Under Periodic Perturbation for 1-d Viscoelasticity with Non-Convex Constitutive Relations
• Traveling Wave Solutions to a Large Class of Brenner-Navier-Stokes-Fourier Systems
• Stability of Riemann Shocks for isothermal Euler by Inviscid limits of global-in-time large Navier-Stokes flows
• Asymptotic behavior toward viscous shocks for the outflow problem of barotropic Navier-Stokes equations
• Uniqueness of a Planar Contact Discontinuity for 3D Compressible Euler System in a Class of Zero Dissipation Limits from Navier–Stokes–Fourier System
• Vanishing viscosity limit to two interacting shocks from the same family for the compressible Navier-Stokes equations