This paper is concerned with the asymptotic stability of the periodic solution to a one-dimensional model system for the compressible viscous van der Waals fluid in Eulerian coordinates.If the initial density and initial momentum are suitably close to the average density and average momentum,then the solution is proved to tend toward a stationary solution as t →∞.
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 L2energy method.
