分野別セミナー

We present a blow-up result for large data for relaxed compressible Navier-Stokes models with a hyperbolization through a nonlinear Cattaneo law for heat conduction as well as through the constitutive Maxwell type relations for the stress tensor. This blow-up occurs in contrast to the situation without relaxation, i.e. for the classical compressible Navier-Stokes equations, where global large solutions exist. It also contrasts the fact that for the linearized system associated to the classical resp. relaxed compressible Navier-Stokes equations, the qualitative behavior is exactly the same: exponential stability in bounded domains and polynomial decay without loss of regularity for the Cauchy problem.