On the Cauchy problem for higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations

Abstract

A family of dispersive equations is considered which links a higher dimensional Benjamin-Ono equation and the Zakharov-Kuznetsov equation. For these fractional Zakharov-Kuznetsov equations new well-posedness results are proved using transversality and localization of time to small frequency dependent time intervals.