Incompressible limit of solutions of multidimensional steady compressible Euler equations

Gui-Qiang G. Chen Academia Sinica, Fudan University, University of Oxford Feimin Huang Academia Sinica Tian-Yi Wang Academia Sinica, Wuhan University of Technology, Chinese University Hong Kong, Gran Sasso Science Institute Wei Xiang City University of Hong Kong

Publications of CMSA of Harvard mathscidoc:1702.38016

A compactness framework is formulated for the incompressible limit of approximate solutions with weak uniform bounds with respect to the adiabatic exponent for the steady Euler equations for compressible fluids in any dimension. One of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass conservation and the vorticity. Another observation is that the incompressibility of the limit for the homentropic Euler flow is directly from the continuity equation, while the incompressibility of the limit for the full Euler flow is from a combination of all the Euler equations. As direct applications of the compactness framework, we establish two incompressible limit theorems for multidimensional steady Euler flows through infinitely long nozzles, which lead to two new existence theorems for the corresponding problems for multidimensional steady incompressible Euler equations.
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@inproceedings{gui-qiangincompressible,
  title={Incompressible limit of solutions of multidimensional steady compressible Euler equations},
  author={Gui-Qiang G. Chen, Feimin Huang, Tian-Yi Wang, and Wei Xiang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207002014776817216},
}
Gui-Qiang G. Chen, Feimin Huang, Tian-Yi Wang, and Wei Xiang. Incompressible limit of solutions of multidimensional steady compressible Euler equations. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207002014776817216.
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