Vanishing Viscosity Limit to Planar Rarefaction Wave with Vacuum for 3D Compressible Navier-Stokes Equations

Authors

  • Xin-Xiang Bian
  • Yi Wang
  • Ling-Ling Xie

DOI:

https://doi.org/10.4208/cmaa.2022-0020

Keywords:

Compressible Navier-Stokes equations, vanishing viscosity limit, rarefaction wave, vacuum.

Abstract

The vanishing viscosity limit of the three-dimensional (3D) compressible and isentropic Navier-Stokes equations is proved in the case that the corresponding 3D inviscid Euler equations admit a planar rarefaction wave solution connected with vacuum states. Moreover, a uniform convergence rate with respect to the viscosity coefficients is obtained. Compared with previous results on the zero dissipation limit to planar rarefaction wave away from vacuum states [27, 28], the new ingredients and main difficulties come from the degeneracy of vacuum states in the planar rarefaction wave in the multi-dimensional setting. Suitable cut-off techniques and some delicate estimates are needed near the vacuum states. The inviscid decay rate around the planar rarefaction wave with vacuum is determined by the cut-off parameter and the nonlinear advection flux terms of 3D compressible Navier-Stokes equations.

Published

2024-03-08

Issue

Section

Articles