Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities

TL;DR

This paper establishes the local well-posedness of the compressible Navier-Stokes equations with density-dependent viscosities in critical Besov spaces, assuming initial density is bounded away from zero.

Contribution

It proves the well-posedness in critical spaces for a class of compressible fluid equations with variable viscosity, under specific initial conditions.

Findings

Proves local well-posedness in critical Besov spaces.

Requires initial density to be bounded away from zero.

Addresses equations with density-dependent viscosities.

Abstract

In this paper, we prove the local well-posedness in critical Besov spaces for the compressible Navier-Stokes equations with density dependent viscosities under the assumption that the initial density is bounded away from zero.