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 G. Farah. Felipe Linares. Ademir Pastor. "Global well-posedness for the $k$-dispersion generalized Benjamin-Ono equation." Differential Integral Equations 27 (7/8) 601 - 612, July/August 2014. https://doi.org/10.57262/die/1399395743