Mathematical Research Letters

Volume 6 (1999)

Number 6

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

Pages: 755 – 778



J. Colliander (University of California at Berkeley)

G. Staffilani (Stanford University)

H. Takaoka (Tohoku University)


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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