Low Mach number limit of the full Navier-Stokes equations,

Thomas Alazard (1)

1 MAB - Laboratoire de Mathématiques Appliquées de Bordeaux

The low Mach number limit for classical solutions of the full Navier-Stokes equations is here studied. The combined effects of large temperature variations and thermal conduction are taken into account. In particular, we consider general initial data. The equations lead to a singular problem whose linearized is not uniformly well-posed. Yet, it is proved that the solutions exist and are uniformly bounded for a time interval which is independent of the Mach number, the Reynolds number and the Péclet number. Based on uniform estimates in Sobolev spaces, and using a Theorem of G. Métivier and S. Schochet, we next prove that the penalized terms converge strongly to zero. This allows us to rigorously justify, at least in the whole space case, the well-known computations given in the introduction of the P.-L. Lions' book.

Domaines: Equations aux dérivées partielles [math.AP]

Thomas Alazard. Low Mach number limit of the full Navier-Stokes equations,. Archive for Rational Mechanics and Analysis, 2005, 180 (1), pp.1-73. ⟨hal-00153152⟩