Global well-posedness of the Benjamin-Ono equation in H1(R)

We show that the Benjamin-Ono equation is globally well-posed in HI(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 H-s for any s [18]. The main new ingredient is to perform a global gauge transformation which almost entirely eliminates this derivative.