Local existence of classical solutions to shallow water equations with Cauchy data containing vacuum

Ben Duan, Zhen Luo, Yuxi Zheng

Research output: Contribution to journalArticle

10 Scopus citations

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 languageEnglish (US)
Pages (from-to)541-567
Number of pages27
JournalSIAM Journal on Mathematical Analysis
Volume44
Issue number2
DOIs
StatePublished - May 28 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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