Well-posedness for a modified two-component Camassa-Holm system in critical spaces
type: Item
instance of: scholarly article
title: Well-posedness for a modified two-component Camassa-Holm system in critical spaces
zbMATH Open document ID: 1270.35204
author: Kai Yan
author: Zhaoyang Yin
published in: Discrete and Continuous Dynamical Systems
publication date: 2013-04-24T00:00:00Z
review text: The authors address local solutions of a two-component generalization of the Camassa-Holm equation. They work in Besov spaces with the critical index \(s = 3/2\). The results can be extended from the case of real line to the case of the periodic domain. The paper consists of three sections. After an introduction, the authors review the construction of Besov spaces, Littlewood-Paley decomposition, and other basic inequalities. In the main Section 3, the authors prove the main result, which guarantees a local well-posedness of the solutions of the two-component Camassa-Holm system in critical Besov spaces. The analysis is based on modified Kato-Picard iterations for quasilinear dispersive wave equations.
reviewed by: Dmitry Pelinovsky
Mathematics Subject Classification ID: 35G25
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
zbMATH DE Number: 6157274
zbMATH Keywords: local well-posedness
zbMATH Keywords: Besov spaces
zbMATH Keywords: critical index
zbMATH Keywords: Littlewood-Paley decomposition
zbMATH Keywords: modified Kato-Picard iterations
MaRDI profile type: Publication
full work available at URL: dcds.2013.33.1699
OpenAlex ID: W2312274755
DOI: 10.3934/DCDS.2013.33.1699
description: scientific article; zbMATH DE number 6157274