 
Summary: LOW MACH NUMBER LIMIT OF THE FULL
NAVIERSTOKES EQUATIONS
THOMAS ALAZARD
Abstract. The low Mach number limit for classical solutions of the full
NavierStokes 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 wellposed. Yet,
it is proved that the solutions exist and are uniformly bounded for a
time interval which is independent of the Mach number Ma (0, 1], the
Reynolds number Re [1, +] and the P´eclet number Pe [1, +].
Based on uniform estimates in Sobolev spaces, and using a Theorem
of G. M´etivier and S. Schochet [30], 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 wellknown computations given in the
introduction of the P.L. Lions' book [26].
Contents
1. Introduction 1
2. Main results 7
3. Localization in the frequency space 10
