Un résultat de compacité sur la densité dans les équations de Navier–Stokes compressibles en domaine variable

Abstract

We present the convergence of (ρnγ) to ργ in compressible isentropic Navier–Stokes equations (Lions, 1996 [6]) in a domain which changes with time. The essential point is to show the convergence a.e. of the density. Following the proof of P.L. Lions, we prove that r=ρlogρ¯−ρlogρ (resp. r=ρ−(ρθ¯)1/θ) is equal to zero. In the case of a moving bondary problem, the main difficulty comes from the non homogeneous boundary condition on u⋅n.