可压缩磁流体动力学流动的大振幅粘性激波的非线性稳定性
Nonlinear stability of large amplitude viscous shock wave for compressible magnetohydrodynamics flows
AI总结：
本文针对可压缩磁流体动力学系统柯西问题，在无需假设粘性激波振幅与速度的情况下，证明了任意大振幅粘性激波在小初始扰动下的时间渐近稳定性，且适用于一般体积粘度，为该领域的稳定性研究提供了关键进展。
AI中文摘要：
在本文中，我们针对可压缩磁流体动力学系统的柯西问题，建立了具有任意大振幅的粘性激波的非线性时间渐近稳定性。与之前依赖于粘性激波振幅和速度的各种小性假设的相关工作不同，此处我们表明，在零质量条件下，任意粘性激波剖面在小初始扰动下是时间渐近稳定的，无需对粘性激波的振幅和速度做任何假设。此外，虽然大多数稳定性结果是针对动量方程中的常粘度获得的，但本结果甚至适用于作为比容的光滑函数的一般体积粘度。证明的关键部分是引入一个新变量，该变量能在比容中提供有效扩散。
英文摘要：
In this article, we establish the nonlinear time-asymptotic stability of viscous shock wave with arbitrary large amplitude to the Cauchy problem for the compressible magnetohydrodynamics system. In contrast to prior related work, which relied on various smallness assumptions on both the amplitude and the speed of the viscous shock wave, here we show that any viscous shock profile is time-asymptotically stable under small initial disturbance with zero mass condition without making any assumptions on the amplitude and speed of the viscous shock wave. Moreover, while most of the stability results are obtained for constant viscosity in the momentum equation, the present results hold even for the general bulk viscosity as a smooth function of specific volume. The key part of the proof is introducing a new variable which provides an effective diffusion in the specific volume.
