Improvement of the parabolic regularization method and applications to dispersive models

Abstract

We prove that the Benjamin–Ono equation is globally well-posed in $H^s\left(R\right)$ for $s>\frac{1}{2}$. Our approach does not rely on the global gauge transformation introduced by Tao (Tao, 2004). Instead, we employ a modified version of the standard parabolic regularization method. In particular, this technique also enables us to establish global well-posedness, in the same Sobolev space, for the dispersion-generalized Benjamin–Ono (DGBO) equation.