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The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation. (English) Zbl 1187.35179
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>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<s3 2 is developed.
MSC:
35Q35PDEs in connection with fluid mechanics
35Q51Soliton-like equations
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35D30Weak solutions of PDE
37N10Dynamical systems in fluid mechanics, oceanography and meteorology
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