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The Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation

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  • Zhaowei Sheng
  • Shaoyong Lai
  • Yuan Ma
  • Xuanjun Luo

Abstract

The existence of global weak solutions to the Cauchy problem for a generalized Camassa-Holm equation with a dissipative term is investigated in the space × ; provided that its initial value belongs to the space . A one-sided super bound estimate and a space-time higher-norm estimate on the first-order derivatives of the solution with respect to the space variable are derived.

Suggested Citation

  • Zhaowei Sheng & Shaoyong Lai & Yuan Ma & Xuanjun Luo, 2012. "The Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-21, October.
    • Handle: RePEc:hin:jnlaaa:693010
    DOI: 10.1155/2012/693010
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