Space-time behavior of the compressible Navier-Stokes equations with hyperbolic heat conduction

Abstract

We consider compressible Navier-Stokes equations with hyperbolic heat conduction in R3. A space-time description of the classical solution is given when the initial perturbation is suitable small. The result implies that all of the unknowns obey the generalized Huygens’ principle as the classical compressible Navier-Stokes equations in Liu and Wang [Commun. Math. Phys. 196, 145–173 (1998)]. Additionally, we show that the decay of the flux q is faster than the other unknowns.