A WELL-POSEDNESS RESULT FOR VISCOUS COMPRESSIBLE FLUIDS WITH ONLY BOUNDED DENSITY

We are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible Navier-Stokes equations. Assuming that the initial velocity has slightly sub-critical regularity and that the initial density is a small perturbation (in the L ∞ norm) of a positive constant, we prove the existence of local-in-time solutions. In the case where the density takes two constant values across a smooth interface (or, more generally, has striated regularity with respect to some nondegenerate family of vector-fields), we get uniqueness. This latter result supplements the work by D. Hoff in [26] with a uniqueness statement, and is valid in any dimension d ≥ 2 and for general pressure laws.Fluides inhomogènes : modèles asymptotiques et évolution d'interfacesBords, oscillations et couches limites dans les systèmes différentielsCommunity of mathematics and fundamental computer science in LyonInteraction Fluide-Structure : Modélisation, analyse, contrôle et simulatio