September  2008, 1(3): 427-460. doi: 10.3934/dcdss.2008.1.427

Navier's slip and incompressible limits in domains with variable bottoms

1. 

Institute of Mathematics AS ČR, Žitná 25, 115 67 Praha 1

2. 

Mathematical Institute of the Charles University, Sokolovská 83, 186 73 Praha 8

3. 

IMATH, Université du Sud Toulon-Var, BP 132, 839 57 La Garde, France

Received  February 2008 Revised  March 2008 Published  June 2008

We consider unsteady flows of compressible Navier-Stokes-Fourier equations in domains with bottoms that are not flat and where the fluid fulfils Navier's slip boundary conditions. Dealing with weak solutions whose long-time and large data existence has been recently established, we investigate their behavior for vanishing Mach number (the square of this small parameter appears also in the Navier slip condition), and prove their convergence towards the weak solution of the so-called Boussinesq approximation with the no-slip boundary condition. The fact that we treat the Navier boundary condition brings several interesting features in the analysis of acoustic waves, in particular the strong convergence of the velocity field.
Citation: Eduard Feireisl, Josef Málek, Antonín Novotný. Navier's slip and incompressible limits in domains with variable bottoms. Discrete & Continuous Dynamical Systems - S, 2008, 1 (3) : 427-460. doi: 10.3934/dcdss.2008.1.427
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