The Asymptotic Stability Of The Model Navier-Stokes2×2 Equations With Two Viscous Sparse Wave Solutions

In this paper,we investigate the model Navier-Stokes equations.We construct the solution o.f rarefaction waves for 2×2 viscous hyperbolic conservation and obtain its-asymptotic stability for the Cauchy problem by energy estimations.There are three chapters in this paper.In the first chapter we give a simple introduction of the history of the asymptotic behavior of the solution of viscous rarefaction waves to the conservation laws with v:iscosity.In the second chapter,we describe the results of others and our main results,Our main result says that if the initial data is close to a constant state and its values at±? lie on the 1,2 rarefaction curve for corresponding Euler equations,then the solution tends as t?? to the viscous rarefaction wave determined by these states.Finally in the third chapter we prove some priori estimates by energy method and then give the proof of our main results by the continuous induction.