The Cauchy problem for the Benjamin–Ono equation inL²revisited

Ionescu and Kenig proved that the Cauchy problem associated with the Benjamin–Ono equation is globally well posed in [math] . 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 [math] for [math] . Note that our approach also permits us to simplify the proof of the global well-posedness in [math] and yields unconditional well-posedness in [math] .