Large data scattering for the defocusing $k$-dispersion generalized Benjamin-Ono equation in the energy space

Abstract

We study the defocusing $k$-dispersion generalized Benjamin-Ono equation. For every even integer $k\ge 4$, we prove that solutions with initial data in the energy space $H^{\frac{\hat{I}}{\pm }2}$ are global in time and scatter. The proof combines the concentration-compactness-rigidity method of Kenig and Merle with techniques based on the Caffarelli-Silvestre extension and Tao's monotonicity formula adapted to the fractional dispersion setting.

33 pages. Comments are welcome !