Weak solutions to the full Navier-Stokes-Fourier system with slip boundary conditions in time dependent domains

We consider the compressible Navier-Stokes-Fourier system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. Assuming that the pressure can be decomposed into an elastic part and a thermal part, we prove global-in-time existence of weak solutions. Our approach is based on the penalization of the boundary behavior, viscosity, and the pressure in the weak formulation. Moreover, the thermal energy equation is in the weak formulation replaced by the thermal energy inequality complemented with the global total energy inequality. In the approximation scheme the thermal energy inequality is consider to be satisfied in the renormalized sense.

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