Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation

2017/01/30 by Ifrim, Mihaela, Tataru, Daniel · 5 citations
#35Q55 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.08476

Abstract

This article represents a first step toward understanding the long time dynamics of solutions for the Benjamin-Ono equation. While this problem is known to be both completely integrable and globally well-posed in L², much less seems to be known concerning its long time dynamics. Here, we prove that for small localized data the solutions have (nearly) dispersive dynamics almost globally in time. An additional objective is to revisit the L² theory for the Benjamin-Ono equation and provide a simpler, self-contained approach.

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