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

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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Cited literature [27 references]

https://hal.archives-ouvertes.fr/hal-00499346
Contributor : Luc Molinet <>
Submitted on : Friday, July 9, 2010 - 11:42:56 AM
Last modification on : Wednesday, June 19, 2019 - 1:26:21 AM
Long-term archiving on : Monday, October 11, 2010 - 9:55:15 AM

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### Identifiers

• HAL Id : hal-00499346, version 1
• ARXIV : 1007.1545

### Citation

Luc Molinet, Didier Pilod. The Cauchy problem for the Benjamin-Ono equation in $L^2$ revisited. Analysis & PDE, Mathematical Sciences Publishers, 2012, 5 (2), pp.365-395. ⟨hal-00499346⟩

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