Local and global well-posedness of dispersion generalized Benjamin-Ono equations on the circle

Abstract

New local well-posedness results for dispersion generalized Benjamin-Ono equations on the torus are proved. The family of equations under consideration links the Benjamin-Ono and Korteweg-de Vries equation. For sufficiently high dispersion global well-posedness in $L^2(\mathbb{T})$ is derived.