Global weak solutions to the Camassa-Holm equation

Zhenhua Guo, Mina Jiang, Zhian Wang, Gao Feng Zheng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


The existence of a global weak solution to the Cauchy problem for a one-dimensional Camassa-Holm equation is established. In this paper, we assume that the initial condition u0 (x) has end states u±, which has much weaker constraints than that u0 (x) ε H1 (ℝ) discussed in [30]. By perturbing the Cauchy problem around a rarefaction wave, we obtain a global weak solution as a limit of viscous approximation under the assumption u- < u+.
Original languageEnglish
Pages (from-to)883-906
Number of pages24
JournalDiscrete and Continuous Dynamical Systems
Issue number3
Publication statusPublished - 1 Jul 2008
Externally publishedYes


  • Camassa-Holm equation
  • Global weak solution
  • Vanishing viscosity method
  • Young measure

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

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