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ON THE LOW REGULARITY SOLUTIONS FOR A MODIFIED TWO-COMPONENT CAMASSA–HOLM SHALLOW WATER SYSTEM

Published online by Cambridge University Press:  10 March 2011

XINGXING LIU  and
ZHAOYANG YIN
XINGXING LIU
Affiliation:
Department of Mathematics, Sun Yat-sen University, 510275 Guangzhou, China e-mail: liuxingxing123456@163.com, mcsyzy@mail.sysu.edu.cn
ZHAOYANG YIN
Affiliation:
Department of Mathematics, Sun Yat-sen University, 510275 Guangzhou, China e-mail: liuxingxing123456@163.com, mcsyzy@mail.sysu.edu.cn
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Abstract

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We first study the regularised version of a modified two-component Camassa–Holm shallow water system and obtain the energy estimates of the corresponding approximate solutions. Then, we present a sufficient condition which guarantees that these approximate solutions converge to a low regularity weak solution of the modified two-component Camassa–Holm shallow water system.

Keywords

35G2535L05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 3 , September 2011 , pp. 611 - 621
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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