Weak solutions to the barotropic Navier-Stokes system with slip boundary conditions in time dependent domains and incompressible limits

We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak formulation. Global-in-time weak solutions are obtained. Secondly, we suppose that the characteristic speed of the fluid is domi- nated by the speed of sound and perform the low Mach number limit in the framework of weak solutions. The standard incompressible Navier-Stokes system is identified as the target problem. References:

[1] E. Feireisl, O. Kreml, S. Nečasová, J. Neustupa, and J. Stebel. Weak solutions to the barotropic NavierStokes system with slip boundary conditions in time dependent domains. J. Differential Equations, 254:125–140, 2013.

[2] E. Feireisl, O. Kreml, S. Nečasová, J. Neustupa, and J. Stebel. Incompressible limits of fluids excited by moving boundaries. Submitted