Asymptotic stability of solutions to the Navier-Stokes-Fourier system driven by inhomogeneous Dirichlet boundary conditions

Abstract

We consider global in time solutions of the Navier-Stokes-Fourier system describing the motion of a general compressible, viscous and heat conducting fluid far from equilibirum. Using a new concept of weak solution suitable to accommodate the inhomogeneous Dirichlet time dependent data we find sufficient conditions for the global in time weak solutions to be ultimately bounded.