On the Free Surface Motion of Highly Subsonic Heat-conducting Inviscid Flows

Tao Luo City University of Hong Kong Huihui Zeng Tsinghua University

Analysis of PDEs mathscidoc:1911.03003

For the free surface problem of the highly subsonic heat-conducting inviscid flow in 2-D and 3-D, a priori estimates for geometric quantities of free surfaces, such as the second fundamental form and the injectivity radius of the normal exponential map, and the Sobolev norms of fluid variables are proved by investigating the coupling of the boundary geometry and the interior solutions. An interesting feature for the free surface problem studied in this paper is the loss of one more derivative than the problem of incompressible Euler equations for which a geometric approach was introduced by Christodoulou and Lindblad in [11]. Due to the loss of one more derivative and loss of symmetry of equations, the geometric approach in [11] needs to be substantially developed by exploring the interaction of large variation of temperature, heat-conduction, non-zero divergence of the fluid velocity and the evolution of free surfaces.
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@inproceedings{taoon,
  title={On the Free Surface Motion of Highly Subsonic Heat-conducting Inviscid  Flows},
  author={Tao Luo, and Huihui Zeng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191128160559186348556},
}
Tao Luo, and Huihui Zeng. On the Free Surface Motion of Highly Subsonic Heat-conducting Inviscid Flows. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191128160559186348556.
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