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Existence of weak solutions in lower order Sobolev space for a Camassa-Holm-type equation. (English) Zbl 1190.35060

Summary: A generalized Camassa-Holm equation containing a nonlinear dissipative effect is investigated. The existence of the weak solution of the equation in lower order Sobolev space \(H^{s}\) with \(1 < s \leqslant \frac{3}{2}\) is established by using the techniques of the pseudoparabolic regularization and some a priori estimates derived from the equation itself.

MSC:

35G25 Initial value problems for nonlinear higher-order PDEs
35Q35 PDEs in connection with fluid mechanics
35B45 A priori estimates in context of PDEs
35D30 Weak solutions to PDEs
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