Abstract: In this talk we consider the Cauchy problem for dispersive generalizations of the Benjamin-Ono equation. To address the nonlinear interactions, we decompose into various frequency regimes and use a variety of tools, including a pseudodifferential generalization of the gauge transform introduced by Tao for the classical Benjamin-Ono equation; paradifferential normal forms inspired by Ifrim-Tataru; and Strichartz estimates on curved backgrounds. This modular approach allows for a much simpler functional setting, and improves the known low regularity well-posedness threshold across the range of the dispersive generalization. This is joint work with Grace Liu.
