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Global Solutions to the Gas-Vacuum Interface Problem of Isentropic Compressible Inviscid Flows with Damping in Spherically Symmetric Motions and Physical Vacuum

Huihui Zeng Tsinghua University, Harvard University CMSA

Publications of CMSA of Harvard mathscidoc:1702.38073

For the physical vacuum free boundary problem with the sound speed being C 1/2 - H¨older continuous near vacuum boundaries of the compressible Euler equations with damping, the global existence of solutions and convergence to Barenblatt self-similar solutions of the porous media equation was recently proved in [34] for 1-d motions by Luo and the author. This paper generalizes the results for 1-d motions to 3-d spherically symmetric motions. Compared with the 1-d theory, besides the high degeneracy of the equations near the physical vacuum boundary, the analytical difficulties lie in the complexity of equations and the coordinates singularity in the center of symmetry which is resolved by constructing suitable weights. The results obtained in this work contribute to the theory of global solutions to free boundary problems of compressible inviscid fluids in the presence of vacuum states, for which the currently available results are mainly for the local-in-time well-posedness theory, also to the theory of global smooth solutions of dissipative hyperbolic systems which fail to be strictly hyperbolic.
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@inproceedings{huihuiglobal,
  title={Global Solutions to the Gas-Vacuum Interface Problem of Isentropic Compressible Inviscid Flows with Damping in Spherically Symmetric Motions and Physical Vacuum},
  author={Huihui Zeng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208004401386053300},
}
Huihui Zeng. Global Solutions to the Gas-Vacuum Interface Problem of Isentropic Compressible Inviscid Flows with Damping in Spherically Symmetric Motions and Physical Vacuum. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208004401386053300.
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