Weak solutions to the barotropic Navier-Stokes system with slip boundary   conditions in time dependent domains
  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. 
Eduard Feireisl, Ond\v{r}ej Kreml, \v{S}\'arka Ne\v{c}asov\'a,   Ji\v{r}\'i Neustupa, Jan Stebel
math.AP