On well-posedness for the Benjamin-Ono equation

Details On well-posedness for the Benjamin-Ono equation On well-posedness for the Benjamin-Ono equation

2005-09-05

arxiv.org/abs/math/0509096v2

Mathematics

Analysis of PDEs

Important changes. We improved both existence and uniqueness results. In particular, uniqueness holds in the natural $L^\infty

Scientific paper

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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