Nonuniform Dependence on Initial Data of a Periodic Camassa-Holm System

This paper is concerned with some properties of a periodic two-component Camassa-Holm system. By constructing two sequences of solutions of the two-component Camassa-Holm system, we prove that the solution map of the Cauchy problem of the two-component Camassa-Holm system is not uniformly continuous...

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Main Author: Xiaohuan Wang
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/823126
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author Xiaohuan Wang
author_facet Xiaohuan Wang
author_sort Xiaohuan Wang
collection DOAJ
description This paper is concerned with some properties of a periodic two-component Camassa-Holm system. By constructing two sequences of solutions of the two-component Camassa-Holm system, we prove that the solution map of the Cauchy problem of the two-component Camassa-Holm system is not uniformly continuous in Hs (𝕊), s>5/2.
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institution Kabale University
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publishDate 2014-01-01
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series Abstract and Applied Analysis
spelling doaj-art-ed173b32f7d943d6bdf9a0fe089cbdbb2025-02-03T01:21:59ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/823126823126Nonuniform Dependence on Initial Data of a Periodic Camassa-Holm SystemXiaohuan Wang0College of Mathematics and Information Science, Henan University, Kaifeng 475001, ChinaThis paper is concerned with some properties of a periodic two-component Camassa-Holm system. By constructing two sequences of solutions of the two-component Camassa-Holm system, we prove that the solution map of the Cauchy problem of the two-component Camassa-Holm system is not uniformly continuous in Hs (𝕊), s>5/2.http://dx.doi.org/10.1155/2014/823126
spellingShingle Xiaohuan Wang
Nonuniform Dependence on Initial Data of a Periodic Camassa-Holm System
Abstract and Applied Analysis
title Nonuniform Dependence on Initial Data of a Periodic Camassa-Holm System
title_full Nonuniform Dependence on Initial Data of a Periodic Camassa-Holm System
title_fullStr Nonuniform Dependence on Initial Data of a Periodic Camassa-Holm System
title_full_unstemmed Nonuniform Dependence on Initial Data of a Periodic Camassa-Holm System
title_short Nonuniform Dependence on Initial Data of a Periodic Camassa-Holm System
title_sort nonuniform dependence on initial data of a periodic camassa holm system
url http://dx.doi.org/10.1155/2014/823126
work_keys_str_mv AT xiaohuanwang nonuniformdependenceoninitialdataofaperiodiccamassaholmsystem