论文标题
一般传入流的可压缩欧拉系统的变化结构和二维亚射流流动
Variational structure and two-dimensional subsonic jet flows for compressible Euler system with general incoming flows
论文作者
论文摘要
在本文中，我们证明了适合的可压缩亚音速射流流的理论，只要通量大于临界值，{\ it一般}传入水平速度的二维稳定Euler系统的水平速度。关键观察之一是，即使流动具有非平凡的涡度，二维可压缩稳定欧拉系统的流函数公式也具有变异结构，以便可以将JET问题重新出现为域变化问题。这种变分结构有助于适应Alt，Caffarelli和Friedman开发的框架，以研究{Jet问题，这是Bernoulli型自由边界问题。分析喷气流量的一个主要技术点是，即使流动的涡度很大，自由边界附近的重新定程方程中的不均匀术语总是很小。
In this paper, we proved the well-posedness theory of compressible subsonic jet flows for two-dimensional steady Euler system with {\it general} incoming horizontal velocity as long as the flux is larger than a critical value. One of the key observations is that the stream function formulation for two-dimensional compressible steady Euler system enjoys a variational structure even when the flows have nontrivial vorticity, so that the jet problem can be reformulated as a domain variation problem. This variational structure helps to adapt the framework developed by Alt, Caffarelli, and Friedman to study {the jet problem, which is a Bernoulli type free boundary problem. A major technical point to analyze the jet flows is that the inhomogeneous terms in the rescaled equation near the free boundary are always small, even when the vorticity of the flows is big.
