The existence and uniqueness of the local solution for a Camassa-Holm type equation |
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Authors: | Shaoyong Lai |
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Affiliation: | Department of Mathematics, Southwestern University of Finance and Economics, 610074 Chengdu, China |
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Abstract: | A shallow water equation of Camassa-Holm type, containing nonlinear dissipative effect, is investigated. Using the techniques of the pseudoparabolic regularization and some prior estimates derived from the equation itself, we establish the existence and uniqueness of its local solution in Sobolev space Hs(R) with . Meanwhile, a new lemma and a sufficient condition which guarantee the existence of solutions of the equation in lower order Sobolev space Hs with are presented. |
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Keywords: | Local well-posedness Generalized Camassa-Holm equation High order nonlinear terms Pseudoparabolic regularization technique |
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