On the Vortex Sheets of Compressible Flows

Robin Ming Chen; Feimin Huang; Dehua Wang; Difan Yuan

doi:10.1007/s42967-022-00191-4

Communications on Applied Mathematics and Computation ›› 2022, Vol. 5 ›› Issue (3) : 967 -986. DOI: 10.1007/s42967-022-00191-4

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On the Vortex Sheets of Compressible Flows

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Abstract

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.

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Robin Ming Chen, Feimin Huang, Dehua Wang, Difan Yuan. On the Vortex Sheets of Compressible Flows. Communications on Applied Mathematics and Computation, 2022, 5(3): 967-986 DOI:10.1007/s42967-022-00191-4