Well-posedness in critical spaces for the system of Navier-Stokes compressible

Abstract

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension $N\ge 2$. We address the question of well-posedness for {\it large} data having critical Besov regularity. Our result improve the analysis of R. Danchin and of B. Haspot, by the fact that we choose initial density more general in $B^{\NN}_{p,1}$ with $1\le p<+\infty$. Our result relies on a new a priori estimate for the velocity, where we introduce a new structure to \textit{kill} the coupling between the density and the velocity. In particular our result is the first where we obtain uniqueness without imposing hypothesis on the gradient of the density.

References in corpus (1)

• Local well-posedness results for density-dependent incompressible fluids