The global weak solution for a generalized Camassa-Holm equation
type: Item
instance of: scholarly article
title: The global weak solution for a generalized Camassa-Holm equation
zbMATH Open document ID: 1282.35336
DOI: 10.1155/2013/838302
author: Shaoyong Lai
published in: Abstract and Applied Analysis
publication date: 2013-05-08T00:00:00Z
review text: Summary: A nonlinear generalization of the famous Camassa-Holm model is investigated. Provided that initial value \(u_0 \in H^s(\mathbb{R})(1 \leq s \leq 3/2)\) and \((1 - \partial^2_x)u_0\) satisfies an associated sign condition, it is shown that there exists a unique global weak solution to the equation in space \(u(t, x) \in L^2([0, +\infty), H^s(\mathbb{R}))\) in the sense of distribution, and \(u_x \in L^\infty([0, +\infty) \times \mathbb{R})\).
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 6161382
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/838302
OpenAlex ID: W2094125788
Wikidata QID: Q58917580
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description: scientific article; zbMATH DE number 6161382