### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 541-567 |

Number of pages | 27 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 44 |

Issue number | 2 |

DOIs | |

State | Published - May 28 2012 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics

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## Cite this

Duan, B., Luo, Z., & Zheng, Y. (2012). Local existence of classical solutions to shallow water equations with Cauchy data containing vacuum.

*SIAM Journal on Mathematical Analysis*,*44*(2), 541-567. https://doi.org/10.1137/100817887