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Zbl 1187.35179
Lai, Shaoyong; Wu, Yonghong
The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation.
(English)
[J] J. Differ. Equations 248, No. 8, 2038-2063 (2010). ISSN 0022-0396

Summary: A generalization of the Camassa-Holm equation, a model for shallow water waves, is investigated. Using the pseudoparabolic regularization technique, its local well-posedness in Sobolev space $H^s(R)$ with $s> \frac 3 2$ is established via a limiting procedure. In addition, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space $H^s$ with $1< s \leqslant \frac{3}{2}$ is developed.
MSC 2000:
*35Q35 Other equations arising in fluid mechanics
35Q51 Solitons
76B15 Wave motions (fluid mechanics)
35D30
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology

Keywords: local well-posedness; weak solution; generalized Camassa-Holm equation; high order nonlinear terms; pseudoparabolic regularization method

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