Mathematical Research Letters

Volume 6, Issue 6, November 1999 pp. 755-778.

Global wellposedness for KdV below ${L^2}$

Authors: J. Colliander, G. Staffilani, and H. Takaoka
Author institution: University of California, Berkeley, Stanford University, and Tohoku University

Summary: The initial value problem for the Korteweg-deVries equation on the line is shown to be globally wellposed for rough data. In particular, we show global wellposedness for certain initial data in $H^s$ for an interval of negative $s$. The proof is an adaptation of a general argument introduced by Bourgain to prove a similar result for a nonlinear Schrödinger equation. The proof relies on a generalization of the bilinear estimate of Kenig, Ponce and Vega.

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