可压缩Navier-Stokes方程行波解的渐近稳定性

Asymptotic stability of solutions for one-dimensional compressible Navier-Stokes equations

研究了一维黏性可压缩Navier-Stokes方程组,给出了在小扰动条件下冲击波解的渐近稳定性。考虑在小的初始扰动下黏性冲击波解的叠加,通过局部解的存在唯一性分析和先验估计,得到此时的黏性冲击波解是渐近稳定的。证明通过能量估计方法给出。

One-dimensional compressible Navier-Stokes equations have been investigated, and the asymptotic stability of the shock wave has been established under conditions of small perturbation. A superposition of the shock wave has been derived under conditions where the initial disturbance is sufficiently small. By the means of existenee and uniqueness of the local solution and the priori estimates, the superposition of the shock wave is shown to have asymptotic stability. The proof is based on the elementary energy method.