Abstract
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 subcritical regularity and that the initial density is a small perturbation (in the 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 (Comm. Pure Appl. Math. 55:11 (2002), 1365–1407) with a uniqueness statement, and is valid in any dimension and for general pressure laws.
Citation
Raphaël Danchin. Francesco Fanelli. Marius Paicu. "A well-posedness result for viscous compressible fluids with only bounded density." Anal. PDE 13 (1) 275 - 316, 2020. https://doi.org/10.2140/apde.2020.13.275
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