Compressible flows: New existence results and justification of the Reynolds asymptotic in thin films

Article type: Research Article

Authors: Chupin, Laurent^; | Sart, Rémy

Affiliations: Laboratoire de Mathématiques, UMR 6620, Université Blaise Pascal, Aubière, France | Ecole Supérieure d'Ingénieurs Léonard de Vinci, Paris La Défense, France

Note: [] Corresponding author: Laurent Chupin, Laboratoire de Mathématiques, UMR 6620, Université Blaise Pascal, Campus des Cézeaux, F-63177 Aubière Cedex, France. E-mail: laurent.chupin@math.univ-bpclermont.fr.

Abstract: In this paper, we are first interested in the compressible Navier–Stokes equations with density dependent viscosities in bounded domains with non-homogeneous Dirichlet conditions. We study the well posedness of such models with density dependent viscosity coefficients in the non-stationary and in the stationary cases. We apply the last result in thin domains context, justifying the compressible Reynolds equations.

Keywords: Navier–Stokes equations, compressible fluids, density dependent viscosities, stationary, steady-state, thin films, lubrication, Reynolds equation

DOI: 10.3233/ASY-2011-1070

Journal: Asymptotic Analysis, vol. 76, no. 3-4, pp. 193-231, 2012