The Local and Global Existence of Solutions for a Generalized Camassa‐Holm Equation

Nan Li, Shaoyong Lai, Shuang Li and Meng Wu

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: A nonlinear generalization of the Camassa‐Holm equation is investigated. By making use of the pseudoparabolic regularization technique, its local well posedness in Sobolev space HS(R) with s > 3/2 is established via a limiting procedure. Provided that the initial value u0 satisfies the sign condition and u0 ∈ Hs(R) (s > 3/2), it is shown that there exists a unique global solution for the equation in space C([0, ∞); Hs(R))∩C1([0, ∞); Hs−1(R)).

Date: 2012
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https://doi.org/10.1155/2012/532369

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:532369

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