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

Raphaël Danchin (1) , Piotr Bogusław Mucha (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Instytut Matematyki Stosowanej i Mechaniki

This paper is concerned with the mathematical derivation of the inhomoge-neous 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, for general initial data. In particular, we are able to handle large variations of density.

Domaines: Equations aux dérivées partielles [math.AP]

Raphaël Danchin, Piotr Bogusław Mucha. From compressible to incompressible inhomogeneous flows in the case of large data. Tunisian Journal of Mathematics, 2019, 1 (1), pp.127-149. ⟨10.2140/tunis.2019.1.127⟩. ⟨hal-01622159⟩