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LOW MACH NUMBER LIMIT OF THE FULL NAVIER-STOKES EQUATIONS
 

Summary: LOW MACH NUMBER LIMIT OF THE FULL
NAVIER-STOKES EQUATIONS
THOMAS ALAZARD
Abstract. 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 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 well-known 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

  

Source: Alazard, Thomas - Département de Mathématiques, Université de Paris-Sud 11

 

Collections: Mathematics