可压Navier-Stokes-Korteweg方程组强稀疏波的稳定性

摘要

We study the asymptotic stability of strong rarefaction waves for the one-dimensional compressible Navier-Stokes-Korteweg equations. Assume that the corresponding Riemann problem to the compressible Euler equations can be solved by rarefaction waves (VR,UR,SR)(t,x) . If the initial data is a small perturbation of an approximate rarefaction wave, we show via the energy method that the Cauchy problem admits a unique global smooth solution which tends to (VR,UR,SR)(t,x) as t tends to infinity.%研究了一维可压Korteweg型流体模型强稀疏波的渐近稳定性问题。假设相应的可压Euler方程的黎曼问题存在稀疏波解( VR ,UR ,SR )( t,x),如果Navier-Stokes-Korteweg系统的初值是近似稀疏波的小扰动,利用能量方法,可以证明其柯西问题存在一个唯一的整体光滑解,并随着时间渐近趋于( VR ,UR , SR )( t,x)。