Local Well-posedness and a priori bounds for the modified Benjamin-Ono equation without using a gauge transformation

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dc.creatorGuo, Zihua
dc.date2008-07-23
dc.date.accessioned2026-07-07T09:52:32Z
dc.date.available2026-07-07T09:52:32Z
dc.descriptionWe prove that the complex-valued modified Benjamin-Ono (mBO) equation is locally wellposed if the initial data $ϕ$ belongs to $H^s$ for $s\geq 1/2$ with $\normϕ_{L^2}$ sufficiently small without performing a gauge transformation. Hence the real-valued mBO equation is globally wellposed for those initial datas, which is contained in the results of C. Kenig and H. Takaoka \cite{KenigT} where the smallness condition is not needed. We also prove that the real-valued $H^\infty$ solutions to mBO equation satisfy a priori local in time $H^s$ bounds in terms of the $H^s$ size of the initial data for $s>1/4$.
dc.description42 pages, 0 figures
dc.identifierhttps://arxiv.org/abs/0807.3764
dc.identifierhttp://arxiv.org/abs/0807.3764
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165630
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.titleLocal Well-posedness and a priori bounds for the modified Benjamin-Ono equation without using a gauge transformation
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