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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.

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