论文标题
物理真空中的可压缩欧拉方程：一种全面的欧拉方法
The compressible Euler equations in a physical vacuum: a comprehensive Eulerian approach
论文作者
论文摘要
本文涉及气体动力学中可压缩的EULER方程的局部适应性问题。对于此系统，我们考虑与物理真空相对应的自由边界问题。尽管对该系统具有明显的身体兴趣，但在高规律性的空间中，对此问题的先前工作仅限于拉格朗日坐标。取而代之的是，本工作的目的是为此问题提供一种新的，充分的欧拉尔方法，该方法在低规律性的Sobolev空间中为这个问题提供了完整的Hadamard风格良好的理论。特别是，我们以尖锐的，规模不变的能量估计和延续标准为数据提供了新的证明，并持续依赖数据。
This article is concerned with the local well-posedness problem for the compressible Euler equations in gas dynamics. For this system we consider the free boundary problem which corresponds to a physical vacuum. Despite the clear physical interest in this system, the prior work on this problemis limited to Lagrangian coordinates, in high regularity spaces. Instead, the objective of the present work is to provide a new, fully Eulerian approach to this problem, which provides a complete, Hadamard style well-posedness theory for this problem in low regularity Sobolev spaces. In particular we give new proofs for both existence, uniqueness, and continuous dependence on the data with sharp, scale invariant energy estimates, and continuation criterion.
