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

Abstract

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.