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Global well-posedness of a system of nonlinearly coupled KdV equations of Majda and Biello

  • Author(s): Guo, Y;
  • Simon, K;
  • Titi, ES
  • et al.
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 H˙s, for s ≥0. Our approach is based on a successive time-averaging method developed by Babin, Ilyin and Titi [A.V. Babin, A.A. Ilyin and E.S. Titi, Commun. Pure Appl. Math., 64(5), 591-648, 2011].

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