Vol. 1, No. 1, 2019

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From compressible to incompressible inhomogeneous flows in the case of large data

Raphaël Danchin and Piotr Bogusław Mucha

Vol. 1 (2019), No. 1, 127–149
Abstract

We are concerned with the mathematical derivation of the inhomogeneous incompressible Navier–Stokes equations (INS) from the compressible Navier–Stokes equations (CNS) in the large volume viscosity limit. We first prove a result of large-time existence of regular solutions for (CNS). Next, as a consequence, we establish that the solutions of (CNS) converge to those of (INS) when the volume viscosity tends to infinity. Analysis is performed in the two-dimensional torus T2 for general initial data. Compared to prior works, the main breakthrough is that we are able to handle large variations of density.

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Keywords
compressible Navier–Stokes equations, inhomogeneous fluids, large volume viscosity limit
Mathematical Subject Classification 2010
Primary: 76N10
Milestones
Received: 19 October 2017
Accepted: 8 January 2018
Published: 2 March 2018
Authors
Raphaël Danchin
Université Paris-Est
LAMA (UMR 8050), UPEMLV, UPEC, CNRS
Créteil
France
Piotr Bogusław Mucha
Instytut Matematyki Stosowanej i Mechaniki
Uniwersytet Warszawski
Warsaw
Poland