Stability and Decay to Zero of the L2-Norms of Perturbations to a Viscous Compressible Heat Conductive Fluid Motion Exterior to a Ball

Abstract.

We consider perturbations to the rest state of heat conductive compressible fluid in a three-dimensional exterior domain. In the regularity class ${\cal V}_s$, we show stability of L ²-norms of these perturbations, while in the more restrictive class ${\cal V}_d$ we show convergence to zero of these perturbations along a time sequence converging to infinity.