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arXiv · 1007.1545

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

Luc Molinet·Didier Pilod
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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 $s>1/4$.

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Luc Molinet, Didier Pilod. 2010-07-09. The Cauchy problem for the Benjamin-Ono equation in $L^2$ revisited. https://arxiv.org/abs/1007.1545

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