Asymptotic stability for one-dimensional motion of non-Newtonian compressible fluids

Abstract

Rarefaction wave solutions for a one-dimensional model system associated with non-Newtonian compressible fluid are investigated in terms of asymptotic stability. The rarefaction wave solution is proved to be asymptotically stable, provided the initial disturbance is suitably small. The proof is given by the elemental L 2 energy method.