The Cauchy problem for the Benjamin-Ono equation in $L^2$ revisited

Luc Molinet; Didier Pilod

The Cauchy problem for the Benjamin-Ono equation in $L^2$ revisited

Analysis of PDEs 2010-07-26 v1

Authors: Luc Molinet , Didier Pilod

Abstract

In a recent work, Ionescu and Kenig proved that the Cauchy problem associatedto the Benjamin-Ono equation is well-posed in $L^2(\mathbb R)$ . In this paper we give a simpler proof of Ionescu and Kenig's result, which moreover provides stronger uniqueness results. In particular, we prove unconditional well-posedness in $H^s(\mathbb R)$ , for $s>1/4$ .

Keywords

Benjamin-Ono equation Cauchy problem well-posedness unconditional well-posedness $L^2$

Cite

@article{arxiv.1007.1545,
  title  = {The Cauchy problem for the Benjamin-Ono equation in $L^2$ revisited},
  author = {Luc Molinet and Didier Pilod},
  journal= {arXiv preprint arXiv:1007.1545},
  year   = {2010}
}

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