Existence result for stationary compressible fluids and asymptotic behavior in thin films

Laurent Chupin (1) , Rémy Sart (2)

1 ICJ - Institut Camille Jordan
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

In this paper, we are first interested in the compressible Navier-Stokes equations with densitydependent viscosities in bounded domains with on-homogeneous Dirichlet conditions. We study the wellposedness of such models with non-constant coefficients in non-stationary and stationary cases. We apply the last result in thin domains context, justifying the compressible Reynolds equations.

Mots clés: Navier-Stokes equations; compressible fluids; density dependent viscosities; stationary; stead state; thin films; lubrication; Reynolds equation

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Laurent Chupin, Rémy Sart. Existence result for stationary compressible fluids and asymptotic behavior in thin films. 2009. ⟨hal-00392488⟩