N. Burq, F. Planchon
Published 2005-09-05, updated 2005-11-25Version 2
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.
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
Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation
Weak solutions, renormalized solutions and enstrophy defects in 2D turbulence
Stability in $H^{1/2}$ of the sum of $K$ solitons for the Benjamin-Ono equation
![QR code for arXiv:math/0509096 [math.AP]](http://oss.arxitics.com/images/favicon.svg)