论文标题
Riemann问题的适应性良好，在一系列消失的物理粘度限制中，具有两次冲击
Well-posedness of the Riemann problem with two shocks for the isentropic Euler system in a class of vanishing physical viscosity limits
论文作者
论文摘要
我们考虑了由1D Euler系统的两种冲击组成的Riemann问题。我们表明，带有两种冲击的Riemann解决方案在弱的无粘性限制的类别中是稳定且独特的，这些解决方案对Navier-Stokes方程的解决方案具有带有有界能量的初始数据。这项工作扩展到了两次冲击的情况下，在一次冲击的情况下，作者的先前结果。它基于加权相对熵的方法，其偏移称为$ a $ contraction理论。由于该方法，一个主要的困难是，班次上几乎无法控制。需要修改移位的构建，以确保在Navier-Stokes系统的水平上，即使受到大型扰动，两种冲击波也很好地分开。这项工作使考虑大量相互作用的波浪所需的基础。解决Bianchini-Bressan猜想的程序是程序的关键结果，这是navier-Stokes方程的无关限制到Euler方程的唯一BV解决方案的情况下，在较小的BV初始值的情况下。
We consider the Riemann problem composed of two shocks for the 1D Euler system. We show that the Riemann solution with two shocks is stable and unique in the class of weak inviscid limits of solutions to the Navier-Stokes equations with initial data with bounded energy. This work extends to the case of two shocks a previous result of the authors in the case of a single shock. It is based on the method of weighted relative entropy with shifts known as $a$-contraction theory. A major difficulty due to the method is that very little control is available on the shifts. A modification of the construction of the shifts is needed to ensure that the two shock waves are well separated, at the level of the Navier-Stokes system, even when subjected to large perturbations. This work put the foundations needed to consider a large family of interacting waves. It is a key result in the program to solve the Bianchini-Bressan conjecture, that is the inviscid limit of solutions to the Navier-Stokes equation to the unique BV solution of the Euler equation, in the case of small BV initial values.
