一维非等温可压缩Navier-Stokes-Korteweg方程组稀疏波的整体稳定性（英文）

Global Stability of Rarefaction Waves for the One-Dimensional Nonisothermal Compressible Navier-Stokes-Korteweg System

可压缩Navier-Stokes-Korteweg方程组可用来描述具有内部毛细作用的粘性可压缩流体的运动.本文研究了毛细系数依赖于密度、粘性系数和热传导系数依赖于温度的一维非等温的可压缩Navier-Stokes-Korteweg方程组Cauchy问题解的大时间行为.利用基本的L2能量方法,我们证明如果相应的Euler方程组的黎曼问题存在稀疏波解,那么所考虑的一维可压缩Navier-Stokes-Korteweg方程组存在唯一的整体强解,并且当时间趋于无穷大时,此强解趋向于稀疏波.这里初始扰动和稀疏波的强度都可以任意大.

This paper is concerned with the large-time behavior of solutions to the Cauchy problem of the one-dimensional nonisothermal compressible Navier-Stokes- Korteweg system with density-dependent capillarity coefficient and temperature-dependent viscosity and heat conductivity coefficients, which models the motions of compressible viscous fluids with internal capillarity. If the corresponding Riemann problem of the compressible Euler system can be solved by a rarefaction wave, we prove that the 1D compressible Navier-Stokes-Korteweg system admits a unique global strong solution which tends to the rarefaction wave as time goes to infinity. Here both the initial perturbation and the strength of the rarefaction wave can be arbitrarily large. The proof is given by an elementary L2 energy method.