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

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

2009-04-08

arxiv.org/abs/0904.1354v1

Mathematics

Analysis of PDEs

Scientific paper

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension $N\geq2$. 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 $1\leq p<+\infty$. 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.

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