1. This paper is devoted to the study of wave fronts of solutions of first order symmetric systems of non-linear partial differential equations. A short communication was published in [4]. The microlocal point of view enables us to obtain more precise information concerning the smoothness of solutions of symmetric hyperbolic systems. Our main result is a generalization to the non-linear case of Theorem 1.1 of Ivriĭ [3]. The machinery of paradifferential operators introduced by Bony [1] together...

This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in ${ℝ}^N$ with $N\ge 2$. We address the question of well-posedness for large and small initial data having critical Besov regularity in functional spaces as close as possible to the ones imposed in the incompressible Navier Stokes system by Cannone, Meyer and Planchon (where $u_0\in B_{p,r}^{\frac{N}{p}-1}$ with $1\le p\<+\infty ,1\le r\le +\infty$). This improves the classical analysis where $u_0$ is considered belonging in $B_{p,1}^{\frac{N}{p}-1}$ such that the velocity $u$ remains...