Title: Asymptotic stability of the superposition of viscous contact wave with rarefaction waves for the compressible Navier-Stokes-Maxwell equations Show Chinese title

Title: 压缩Navier-Stokes-Maxwell方程组粘性接触波与稀疏波叠加的渐近稳定性

Abstract: We study the large-time asymptotic behavior of solutions toward the combination of a viscous contact wave with two rarefaction waves for the compressible non-isentropic Navier-Stokes equations coupling with the Maxwell equations through the Lorentz force (called the Navier-Stokes-Maxwell equations). It includes the electrodynamic effects into the dissipative structure of the hyperbolic-parabolic system and turns out to be more complicated than that in the simpler compressible Navier-Stokes equations. Based on a new observation of the specific structure of the Maxwell equations in the Lagrangian coordinates, we prove that this typical composite wave pattern is time-asymptotically stable for the Navier-Stokes-Maxwell equations under some smallness conditions on the initial perturbations and wave strength, and also under the assumption that the dielectric constant is bounded. The main result is proved by using elementary energy methods. This is the first result about the nonlinear stability of the combination of two different wave patterns for the compressible Navier-Stokes-Maxwell equations. Show Chinese abstract

Abstract: 我们研究了可压缩非等熵Navier-Stokes方程与通过洛伦兹力耦合的麦克斯韦方程组（称为Navier-Stokes-Maxwell方程）的解在长时间后的渐近行为，针对粘性接触波与两个稀疏波的组合。它将电磁效应纳入双曲-抛物系统的耗散结构中，并显示出比更简单的可压缩Navier-Stokes方程中更为复杂的特性。基于对拉格朗日坐标下麦克斯韦方程组特定结构的新观察，我们在初始扰动和波强度满足某些小性条件以及介电常数有界假设下，证明了这种典型的复合波模式对于Navier-Stokes-Maxwell方程是时间渐近稳定的。主要结果是通过使用基本的能量方法证明的。这是关于可压缩Navier-Stokes-Maxwell方程中两种不同波模式组合的非线性稳定性的第一个结果。