Global well-posedness for the k-dispersion generalized Benjamin-Ono equation (1212.4445v1)

Abstract: We consider the $k$-dispersion generalized Benjamin-Ono equation in the supercritical case. We establish sharp conditions on the data to show global well-posedness in the energy space for this family of nonlinear dispersive equations. We also prove similar results for the generalized Benjamin-Ono equation.