Uniform well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

Zihua Guo, Lizhong Peng, Baoxiang Wang, Yuzhao Wang

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13 Citations (Scopus)

Abstract

We prove that the Cauchy problem for the Benjamin-Ono-Burgers equation is uniformly globally well-posed in Hs (s? 1) for all ??[0,1]. Moreover, we show that as ??0 the solution converges to that of Benjamin-Ono equation in C([0,T]:Hs) (s?1) for any T>0. Our results give an alternative proof for the global well-posedness of the BO equation in H1(R) without using gauge transform, which was first obtained by Tao (2004) [23], and also solve the problem addressed in Tao (2004) [23] about the inviscid limit behavior in H1.
Original languageEnglish
Pages (from-to)647 - 677
Number of pages31
JournalAdvances in Mathematics
Volume228
Issue number2
DOIs
Publication statusPublished - 2011
Externally publishedYes

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