Nonlinear stability of traveling wave solutions for the compressible fluid models of Korteweg type

作者：Chen, Zhengzheng; He, Lin^*; Zhao, Huijiang

来源：Journal of Mathematical Analysis and Applications, 2015, 422(2): 1213-1234.

DOI：10.1016/j.jmaa.2014.09.050

• Navier-Stokes-Korteweg system
• Traveling wave solutions
• Nonlinear stability
• L-2-energy estimates

This paper is concerned with the existence and time-asymptotic nonlinear stability of traveling wave solutions to the Cauchy problem of the one-dimensional compressible fluid models of Korteweg type, which governs the motions of the compressible fluids with internal capillarity. The existence of traveling wave solutions is obtained by the phase plane analysis, then the traveling wave solution is shown to be asymptotically stable by the elementary L-2-energy method.

• 出版日期2015-2-15
• 单位安徽大学; 武汉大学