Weak-strong uniqueness for compressible Navier-Stokes system with slip   boundary conditions on time dependent domains
  We consider the compressible Navier-Stokes system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. We derive the relative entropy inequality in the spirit of Feireisl et al. for the system on moving domain and use it to prove the weak-strong uniqueness property. 
Ond\v{r}ej Kreml, \v{S}\'arka Ne\v{c}asov\'a and Tomasz Piasecki
math.AP