On the Vortex Sheets of Compressible Flows
On the Vortex Sheets of Compressible Flows
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DOI：
10.1007/s42967-022-00191-4
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发表时间：
2022-05
影响因子：
1.6
通讯作者：
R. Chen;F. Huang;Dehua Wang;Difan Yuan
中科院分区：
文献类型：
--
作者：
R. Chen;F. Huang;Dehua Wang;Difan Yuan
本文综述了可压缩流动中涡片稳定性的最新研究成果。涡片是下伏流动的接触不连续。涡片问题是一个具有特征边界的自由边界问题，在分析中具有挑战性。文中将介绍涡片问题的公式。总结了二维两相可压缩流动和二维弹性流动的线性稳定性和非线性稳定性。文中还给出了三维弹性流动涡片的线性稳定性。讨论了涡片问题的难点和证明的思路。
This paper provides a review of the recent results on the stability of vortex sheets in compressible flows. Vortex sheets are contact discontinuities of the underlying flows. The vortex sheet problem is a free boundary problem with a characteristic boundary and is challenging in analysis. The formulation of the vortex sheet problem will be introduced. The linear stability and nonlinear stability for both the two-dimensional two-phase compressible flows and the two-dimensional elastic flows are summarized. The linear stability of vortex sheets for the three-dimensional elastic flows is also presented. The difficulties of the vortex sheet problems and the ideas of proofs are discussed.