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Zbl 1205.76049
Yin, Zheng; Lai, Shaoyong; Guo, Yunxi
Global existence of weak solutions for a shallow water equation. (English)
[J] Comput. Math. Appl. 60, No. 9, 2645-2652 (2010). ISSN 0898-1221

Summary: A nonlinear shallow water equation, which includes the famous Camassa-Holm (CH) and Degasperis-Procesi (DP) equations as special cases, is investigated. Provided that initial value $u_{0}\in H^s$ $(1\le s \le\frac32)$, $u_o\in L^{1}(R)$ and $(1-\delta_x^2)u_0$ does not change sign, it is shown that there exists a unique global weak solution to the equation.

MSC 2000:: *76B03 Existence, uniqueness, and regularity theory
35Q35 Other equations arising in fluid mechanics

Keywords: global existence; blow-up; shallow water model; local well-posedness

Cited in: Zbl 1222.35064

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