On well-posedness for the Benjamin-Ono equation

N. Burq; F. Planchon

On well-posedness for the Benjamin-Ono equation

Analysis of PDEs 2007-05-23 v2

Authors: N. Burq , F. Planchon

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.

Keywords

benjamin-ono equation

Cite

@article{arxiv.math/0509096,
  title  = {On well-posedness for the Benjamin-Ono equation},
  author = {N. Burq and F. Planchon},
  journal= {arXiv preprint arXiv:math/0509096},
  year   = {2007}
}

Comments

Important changes. We improved both existence and uniqueness results. In particular, uniqueness holds in the natural $L^\infty_t; H^{1/2}_x$ energy space

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