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2020 A well-posedness result for viscous compressible fluids with only bounded density
Raphaël Danchin, Francesco Fanelli, Marius Paicu
Anal. PDE 13(1): 275-316 (2020). DOI: 10.2140/apde.2020.13.275

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 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 (Comm. Pure Appl. Math. 55:11 (2002), 1365–1407) with a uniqueness statement, and is valid in any dimension d2 and for general pressure laws.

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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

Information

Received: 24 April 2018; Accepted: 30 November 2018; Published: 2020
First available in Project Euclid: 16 January 2020

zbMATH: 07171994
MathSciNet: MR4047647
Digital Object Identifier: 10.2140/apde.2020.13.275

Subjects:
Primary: 35Q35
Secondary: 35A02 , 35B30 , 35B65 , 76N10

Keywords: bounded density , compressible Navier–Stokes equations , Lagrangian formulation , maximal regularity , tangential regularity

Rights: Copyright © 2020 Mathematical Sciences Publishers

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