Global well-posedness and inviscid limit for the generalized Benjamin–Ono–Burgers equation

Abstract

ABSTRACT This paper deals with the Cauchy problem for the generalized Benjamin–Ono–Burgers equation , , where denotes Hilbert transform. We obtain its global well-posedness results in Besov Spaces if and the initial data in are sufficiently small, where corresponds to the critical scaling regularity index. Furthermore, we prove its global well-posedness and inviscid limit behavior in Sobolev spaces.