The cauchy problem for the benjamin-ono equation in L2R revisited

Abstract

Ionescu and Kenig proved that the Cauchy problem associated with the Benjamin-Ono equation is globally well posed in L2(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 Hs(ℝ). for s > 1/4 . Note that our approach also permits us to simplify the proof of the global well-posedness in L2(T) and yields unconditional well-posedness in H1/2(T).