The local strong and weak solutions for a nonlinear dissipative Camassa-Holm equation
type: Item
instance of: scholarly article
title: The local strong and weak solutions for a nonlinear dissipative Camassa-Holm equation
zbMATH Open document ID: 1228.35204
DOI: 10.1155/2011/285040
author: Shaoyong Lai
published in: Abstract and Applied Analysis
publication date: 2011-10-27T00:00:00Z
review text: Summary: Using the Kato theorem for abstract differential equations, the local well-posedness of the solution for a nonlinear dissipative Camassa-Holm equation is established in space \(C([0, T), H^s(R)) \cap C^1([0, T), H^{s-1}(R))\) with \(s > 3/2\). In addition, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space \(H^s(R)\) with \(1 \leq s \leq 3/2\) is developed.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 5964386
zbMATH Keywords: Camassa-Holm equation
Wikidata QID: Q58654109
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/285040
OpenAlex ID: W2085874702
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description: scientific article; zbMATH DE number 5964386