THE CAUCHY PROBLEM FOR THE BENJAMIN-ONO EQUATION IN L2 REVISITED

Ionescu and Kenig proved that the Cauchy problem associated with the Benjamin-Ono equation is globally well posed in L-2 (R). In this paper we give a simpler proof of Ionescu and Kenig's result, which moreover provides stronger uniqueness results. In particular, we prove unconditional well-posedness in H-s (R) for s > 1/4. Note that our approach also permits us to simplify the proof of the global well-posedness in L-2 (T) and yields unconditional well- posedness in H-1/2 (T).