Well-posedness of the periodic dispersion-generalized Benjamin-Ono equation in the weakly dispersive regime

Abstract

We study the dispersion-generalized Benjamin-Ono equation in the periodic setting. This equation interpolates between the Benjamin-Ono equation ($α=1$) and the viscous Burgers' equation ($α=0$). We obtain local well-posedness in $H^s$ for $s>3/2-α$