Vanishing viscosity limit for the compressible Navier-Stokes equations with non-linear density dependent viscosities

TL;DR

This paper establishes criteria under which weak solutions of the compressible Navier-Stokes equations with nonlinear density-dependent viscosities converge to strong solutions of the Euler system as viscosity and drag parameters vanish.

Contribution

It introduces two conditional Kato-type criteria for the convergence of solutions in a 3D bounded domain with nonlinear viscosities and drag effects.

Findings

Derived Kato-type convergence criteria for weak to strong solution transition.

Analyzed the vanishing viscosity limit in the presence of nonlinear density-dependent viscosities.

Extended understanding of the compressible Navier-Stokes to Euler limit in complex settings.

Abstract

In a three-dimensional bounded domain $\Omega$ we consider the compressible Navier-Stokes equations for a barotropic fluid with general non-linear density dependent viscosities and no-slip boundary conditions. A nonlinear drag term is added to the momentum equation. We establish two conditional Kato-type criteria for the convergence of the weak solutions to such a system towards the strong solution of the compressible Euler system when the viscosity coefficient and the drag term parameter tend to zero.