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

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

2010-07-09

arxiv.org/abs/1007.1545v1

Mathematics

Analysis of PDEs

Scientific paper

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 $s>1/4$.

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