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THE INVISCID LIMIT OF THE MODIFIED BENJAMIN–ONO–BURGERS EQUATION

Part of: Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  06 December 2010

HUA ZHANG  and
YUQIN KE
HUA ZHANG*
Affiliation:
College of Sciences, North China University of Technology, Beijing 100144, PR China (email: zhanghuamaths@163.com)
YUQIN KE
Affiliation:
Faculty of Economics, Guangdong University of Business Studies, Guangzhou 510320, PR China (email: keyuqin@gmail.com)
*
✉For correspondence; e-mail: zhanghuamaths@163.com
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Abstract

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We prove that the modified Benjamin–Ono–Burgers equation is globally well-posed in Hs for s>0. Moreover, we show that the solution of the modified Benjamin–Ono–Burgers equation converges to that of the modified Benjamin–Ono equation in the natural space C([0,T];Hs), s≥1/2, as the dissipative coefficient ϵ goes to zero, provided that the L2 norm of the initial data is sufficiently small.

Keywords

modified Benjamin–Ono–Burgers equationglobal well-posednessinviscid limit

MSC classification

Secondary: 35Q53: KdV-like equations (Korteweg-de Vries)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 2 , April 2011 , pp. 301 - 320
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

Zhang was partially supported by the Science Research Startup Foundation of North China University of Technology.

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