论文标题
1-D完整可压缩的Navier-Stokes方程的两个粘性冲击的复合波的周期性扰动
Periodic perturbations of a composite wave of two viscous shocks for 1-D full compressible Navier-Stokes equations
论文作者
论文摘要
本文涉及在1-D完整可压缩的Navier-Stokes方程的空间周期性扰动下进行两次粘性冲击的复合波的渐近稳定性。事实证明，随着时间的增加，解决方案会以每次冲击的变化方式接近背景复合波，在这种情况下，如果两种冲击的周期性扰动和强度都很小，则可以唯一确定偏移。证明的关键是构建合适的ANSATZ，以便抗衍生方法有效。
This paper is concerned with the asymptotic stability of a composite wave of two viscous shocks under spatially periodic perturbations for the 1-D full compressible Navier-Stokes equations. It is proved that as time increases, the solution approaches the background composite wave with a shift for each shock, where the shifts can be uniquely determined if both the periodic perturbations and strengths of two shocks are small. The key of the proof is to construct a suitable ansatz such that the anti-derivative method works.
