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

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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compressible Navier–Stokes equations, inhomogeneous fluids, large volume viscosity limit
Mathematical Subject Classification 2010
Primary: 76N10
Received: 19 October 2017
Accepted: 8 January 2018
Published: 2 March 2018
Raphaël Danchin
Université Paris-Est
Piotr Bogusław Mucha
Instytut Matematyki Stosowanej i Mechaniki
Uniwersytet Warszawski