Global well-posedness of the Benjamin-Ono equation in low-regularity spaces

Abstract

We prove that the Benjamin-Ono initial value problem is globally well-posed in the Sobolev spaces $H_r^{\sigma }$, $\sigma \ge 0$.

References in corpus (1)

• Global regularity of wave maps II. Small energy in two dimensions

Cited by in corpus (6)

• Ill-posedness issues for nonlinear dispersive equations
• An improved bilinear estimate for Benjamin-Ono type equations
• Global behaviour of nonlinear dispersive and wave equations
• Global wellposedness of the modified Benjamin-Ono equation with initial data in $H^{1/2}$
• Global existence and uniqueness of Schrödinger maps in dimensions $d\ge 4$
• On finite energy solutions of the KP-I equation