Inviscid limit for the compressible Navier-Stokes equations with density dependent viscosity

TL;DR

This paper proves that solutions to the compressible Navier-Stokes equations with density-dependent viscosity converge to solutions of the Euler equations as viscosity and damping vanish, enhancing understanding of fluid behavior in limiting regimes.

Contribution

It establishes the convergence of weak solutions of the compressible Navier-Stokes system to strong solutions of the Euler system under vanishing viscosity and damping.

Findings

Weak solutions converge to Euler solutions as viscosity tends to zero

Density-dependent viscosity is effectively handled in the convergence analysis

Results apply to three-dimensional bounded domains

Abstract

We consider the compressible Navier-Stokes system describing the motion of a barotropic fluid with density dependent viscosity confined in a three-dimensional bounded domain $\Omega$. We show the convergence of the weak solution to the compressible Navier-Stokes system to the strong solution to the compressible Euler system when the viscosity and the damping coefficients tend to zero.