  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.
