Abstract
We consider the Navier–Stokes–Fourier system describing the motion of a compressible, viscous, and heat-conducting fluid in a bounded domain , d = 2, 3, with general non-homogeneous Dirichlet boundary conditions for the velocity and the absolute temperature, with the associated boundary conditions for the density on the inflow part. We introduce a new concept of a weak solution based on the satisfaction of the entropy inequality together with a balance law for the ballistic energy. We show the weak–strong uniqueness principle as well as the existence of global-in-time solutions.
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