Local Existence of Classical Solutions to Shallow Water Equations with Cauchy Data Containing Vacuum

@article{Duan2012LocalEO,
  title={Local Existence of Classical Solutions to Shallow Water Equations with Cauchy Data Containing Vacuum},
  author={Ben Duan and Zhenguo Luo and Yuxi Zheng},
  journal={SIAM J. Math. Anal.},
  year={2012},
  volume={44},
  pages={541-567}
}
In this paper, we investigate the Cauchy problem for the rotating shallow water equations with physical viscosity. We obtain the local existence of classical solutions without assuming the initial height is small or a small perturbation of some constant status. Moreover, the initial vacuum is allowed and the spatial measure of the set of vacuum can be arbitrarily large. In particular, the initial height can even have compact support; in this case, a blow-up example is given. 
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13 Citations

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