GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H1(R)

We show that the Benjamin–Ono equation is globally well-posed in Hs(R) for s≥1. This is despite the presence of the derivative in the nonlinearity, which causes the solution map to not be uniformly continuous in Hs for any s [18]. The main new ingredient is to perform a global gauge transformation which almost entirely eliminates this derivative.