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On the Vortex Sheets of Compressible Flows

Communications on Applied Mathematics and Computation 2023年第3期5卷 967-986页

作者： Robin Ming Chen Feimin Huang Dehua Wang Difan Yuan Department of Mathematics University of PittsburghPittsburghPA 15260USA School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Institute of Applied Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences Beijing Normal University and Laboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875China

This paper provides a review of the recent results on the stability of vortex sheets in compressible *** sheets are contact discontinuities of the underlying *** vortex sheet problem is a free boundary problem with a characteristic boundary and is challenging in *** formulation of the vortex sheet problem will be *** linear stability and nonlinear stability for both the two-dimensional two-phase compressible flows and the two-dimensional elastic flows are *** linear stability of vortex sheets for the three-dimensional elastic flows is also *** difficulties of the vortex sheet problems and the ideas of proofs are discussed.

关键词： Vortex sheets Contact discontinuities stability and instability Loss of derivatives Two-phase flows Elastic flows

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Principle Question of Harmonic Quantitative Analysis of Spectrum Expansion

引用

Engineering Sciences 2005年第3期 40-43页

作者： OuYang Shoucheng1, Wei Ming2(1. Chengdu University of Information Technology, Chengdu 610041 2. Nanjing Sino-America Cooperative Remote Sensing Laboratory,Jiangsu Key Lab.of Meteorological Disaster,Nanjing University of Information Saience & Technology,Nanjing 210044)

The numerical analysis was made in terms of questions that quantity is stable or unstable. The results show that the stability due to “infinitesimal difference of they are well-matched in large quantity" or “Chaos" leads to numerical calculation meaningless. The quantity instability due to magnitude explosive increasing does not follow the suitability. Both unstable magnitude be restricted by the suitability and the numerical calculating by “ill-posed equation" of “infinitesimal difference of they are well-matched in large quantity" might fall into producing false information.

关键词： stability and instability “ill-posed equation" false information

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