Global Well-posedness of a System of Nonlinearly Coupled KdV equations of Majda and Biello

Abstract

This paper addresses the problem of global well-posedness of a coupled system of Korteweg-de Vries equations, derived by Majda and Biello in the context of nonlinear resonant interaction of Rossby waves, in a periodic setting in homogeneous Sobolev spaces $\dot H^s$, for $s\geq 0$. Our approach is based on a successive time-averaging method developed by Babin, Ilyin and Titi [1].