Abstract
We consider the non-isentropic compressible Navier-Stokes equations with hyperbolic heat conduction and a law for the stress tensor which is modified correspondingly by Maxwell's law. These two relaxations, turning the whole system into a hyperbolic one, are not only treated simultaneously, but are also considered in a version having Galilean invariance. For this more complicated relaxed system, the global well-posedness is proved for small data. Moreover, for vanishing relaxation parameters the solutions are shown to converge to solutions of the classical system.
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