Stability of planar rarefaction waves in the vanishing dissipation limit of the Navier-Stokes-Fourier system

2024/04/16 by Eduard Feireisl, Feireisl, Eduard, Wladimir Neves +1
Earth and Planetary Sciences · Mathematics · #35Q35 #76N06 #76N10 #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2404.10604

openalex publication_date 2024/04/16 · openalex created_date 2024/04/18 · openalex updated_date 2026/08/01

Abstract

We consider the vanishing dissipation limit of the compressible Navier-Stokes-Fourier system, where the initial data approach a profile generating a planar rarefaction wave for the limit Euler system. We show that the associated weak solutions converge unconditionally to the planar rarefaction wave strongly in the energy norm.

Related

• Stability of the planar rarefaction wave to two-dimensional compressible Navier-Stokes equations
• Vanishing dissipation limit to the planar rarefaction wave for the three-dimensional compressible Navier-Stokes-Fourier equations
• Asymptotic stability of rarefaction waves for compressible Navier-Stokes equations with relaxation
• Stability of planar rarefaction wave to 3D full compressible Navier-Stokes equations
• Stability of rarefaction waves of the Navier-Stokes-Poisson system