The Regularity of Semihyperbolic Patches Near Sonic Lines for The 2-D Euler System in Gas Dynamics

@article{Song2015TheRO,
  title={The Regularity of Semihyperbolic Patches Near Sonic Lines for The 2-D Euler System in Gas Dynamics},
  author={Kyungwoo Song and Qin Wang and Yuxi Zheng},
  journal={SIAM J. Math. Anal.},
  year={2015},
  volume={47},
  pages={2200-2219}
}
We study the regularity of semihyperbolic patches of self-similar solutions near sonic lines to a Riemann problem for the two-dimensional (2-D) Euler system. As a result, it is verified that there exists a global solution in the semihyperbolic patch up to the sonic boundary and that the sonic boundary has $C^1$-regularity. The study of the semihyperbolic patches of solutions for the Euler system was initiated by Li and Zheng [Arch. Rational Mech. Anal., 201 (2011), pp. 1069--1096]. This type of… 

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