Communications in Mathematical Sciences

Volume 13 (2015)

Number 5

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

Pages: 1261 – 1288

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n5.a9

Authors

Yanqiu Guo (Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel)

Konrad Simon (Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel)

Edriss S. Titi (Department of Mathematics, Texas A&M University, College Station, Tx., U.S.A.; and Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel)

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 [A.V. Babin, A.A. Ilyin and E.S. Titi, Commun. Pure Appl. Math., 64(5), 591-648, 2011].

Keywords

KdV equation, global well-posedness, successive time-averaging method

2010 Mathematics Subject Classification

35B34, 35Q53

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