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Well-posedness of the Free Boundary Problem for Non-relativistic and Relativistic Compressible Euler Equations with a Vacuum Boundary Condition

机译:具有真空边界条件的非相对论和相对论可压缩欧拉方程的非相对论和相对论可压缩欧拉方程的良好介绍

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We survey recent results [7] for the free boundary problem for the equations of compressible Euler equations with a vacuum boundary condition. We consider the case when the density does not go to zero continuously, but jumps. We recover in Eulerian coordinates the earlier well-posedness result obtained by Lindblad [4] for the isentropic Euler equations and extend it to the case of full gas dynamics. Our approach is still directly applicable to the relativistic version of the problem in the setting of special relativity. We also briefly discuss open problems for the general relativistic case and their solution in the framework of relativistic magnetohydrodynamics (plasma-vacuum interface problem [9]).
机译:对于具有真空边界条件的可压缩欧拉方程式的自由边界问题,我们调查了最近的结果[7]。我们考虑密度不连续归零的情况,但跳跃。我们在Eulerian中恢复坐标,Lindblad [4]对于等式欧拉方程,将其获得的早期良好的良好结果进行延伸,并将其扩展到全部气体动态的情况。我们的方法仍然是直接适用于特殊相对性的解决方案的相对论。我们还简要介绍了在相对论磁力流体动力学框架中讨论了一般相对论的案例及其解决方案(等离子体 - 真空界面问题[9])。

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