Asymptotic stability of strong rarefaction waves for the compressible fluid models of Korteweg type
- 作者：Zhengzheng Chen chenzzandu@163.com
- 关键词：Navier&ndash ; Stokes&ndash ; Korteweg system ; Strong rarefaction wave ; Nonlinear stability ; L2 energy estimates ; Continuation argument
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2012
- 期刊代码：76_0022247x
- 类别：mt
- 出版时间：1 October, 2012
- 卷：394
- 期：1
- 页码：438-448
- 文件大小：247 K
摘要
This paper is concerned with the time-asymptotic behavior toward strong rarefaction waves of solutions to one-dimension compressible fluid models of Korteweg type, which governs the motions of the compressible fluids with internal capillarity. Assume that the corresponding Riemann problem to the compressible Euler system can be solved by rarefaction waves . If the initial data is a small perturbation of an approximate rarefaction wave for , we show that the corresponding Cauchy problem admits a unique global smooth solution which tends to time asymptotically. Since we do not require the strength of the rarefaction waves to be small, this result gives the nonlinear stability of strong rarefaction waves for the one-dimensional compressible fluid models of Korteweg type. The analysis is based on the elementary energy method together with continuation argument.