Global well-posedness for the k-dispersion generalized Benjamin-Ono   equation
  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. 
Luiz Gustavo Farah, Felipe Linares, and Ademir Pastor
math.AP