Global well-posedness and inviscid limit for the Korteweg-de Vries-Burgers equation

Zihua Guo, Baoxiang Wang

Research output: Contribution to journalArticleResearchpeer-review

29 Citations (Scopus)

Abstract

Considering the Cauchy problem for the Korteweg-de Vries-Burgers equationut + ux x x + ? lunate ?x 2 ? u + (u2)x = 0, u (0) = ? symbol , where 0 <? lunate , ? ? 1 and u is a real-valued function, we show that it is globally well-posed in Hs (s > s?), and uniformly globally well-posed in Hs (s > - 3 / 4) for all ? lunate ? (0, 1]. Moreover, we prove that for any T > 0, its solution converges in C ([0, T] ; Hs) to that of the KdV equation if ? lunate tends to 0.
Original languageEnglish
Pages (from-to)3864 - 3901
Number of pages38
JournalJournal of Differential Equations
Volume246
Issue number10
DOIs
Publication statusPublished - 2009
Externally publishedYes

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