We prove existence of solutions for the Benjamin-Ono equation with data in
Hs(R), s>0. Thanks to conservation laws, this yields global solutions for
H21​(R) data, which is the natural ``finite energy'' class. Moreover,
inconditional uniqueness is obtained in Lt∞​(H21​(R)), which
includes weak solutions, while for s>203​, uniqueness holds in a
natural space which includes the obtained solutions.Comment: Important changes. We improved both existence and uniqueness results.
In particular, uniqueness holds in the natural Lt∞​;Hx1/2​ energy
spac