Browsing by Author "Danchin, Raphaël"

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    A Well-Posedness Result for Viscous Compressible Fluids with Only Bounded Density
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2018) Danchin, Raphaël; Fanelli, Francesco; Paicu, Marius
    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 th 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.