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Subsonic-sonic limit of approximate solutions to multidimensional steady euler equations

Gui-Qiang Chen Fudan University, University of Oxford, Academia Sinica Fei-Min Huang Academia Sinica Tian-Yi Wang Wuhan University of Technology, Academia Sinica, University of Oxford

Publications of CMSA of Harvard mathscidoc:1702.38017

A compactness framework is established for approximate solutions to subsonicsonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional irrotational case do not directly apply for the steady full Euler equations in higher dimensions. The new compactness framework we develop applies for both non-homentropic and rotational flows. One of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass balance and the vorticity, along with the Bernoulli law and the entropy relation, through a more delicate analysis on the phase space. As direct applications, we establish two existence theorems for multidimensional subsonic-sonic full Euler flows through infinitely long nozzles.
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@inproceedings{gui-qiangsubsonic-sonic,
  title={SUBSONIC-SONIC LIMIT OF APPROXIMATE SOLUTIONS TO MULTIDIMENSIONAL STEADY EULER EQUATIONS},
  author={Gui-Qiang Chen, Fei-Min Huang, and Tian-Yi Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207002237218560217},
}
Gui-Qiang Chen, Fei-Min Huang, and Tian-Yi Wang. SUBSONIC-SONIC LIMIT OF APPROXIMATE SOLUTIONS TO MULTIDIMENSIONAL STEADY EULER EQUATIONS. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207002237218560217.
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