The Global Weak Solution for a Generalized Camassa‐Holm Equation

Shaoyong Lai

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: A nonlinear generalization of the famous Camassa‐Holm model is investigated. Provided that initial value u0 ∈ Hs(R)(1 ≤ s ≤ 3/2) and (1-∂x2)u0 satisfies an associated sign condition, it is shown that there exists a unique global weak solution to the equation in space u(t, x) ∈ L2([0, +∞), Hs(R)) in the sense of distribution, and ux ∈ L∞([0, +∞) × R).

Date: 2013
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https://doi.org/10.1155/2013/838302

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:838302

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