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On well-posedness for the Benjamin-Ono equation

N. Burq·F. Planchon
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Abstract

We prove existence of solutions for the Benjamin-Ono equation with data in $H^s(\R)$, $s>0$. Thanks to conservation laws, this yields global solutions for $H^\frac 1 2(\R)$ data, which is the natural ``finite energy'' class. Moreover, inconditional uniqueness is obtained in $L^\infty_t(H^\frac 1 2(\R))$, which includes weak solutions, while for $s>\frac 3 {20}$, uniqueness holds in a natural space which includes the obtained solutions.

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N. Burq, F. Planchon. 2005-11-25. On well-posedness for the Benjamin-Ono equation. https://arxiv.org/abs/math/0509096

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