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

J. Colliander, Gigliola Staffilani, Hideo Takaoka

Type: Article

Publication Date: 1999-01-01

Citations: 40

DOI: https://doi.org/10.4310/mrl.1999.v6.n6.a13

Abstract

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.

Locations

Mathematical Research Letters - View - PDF

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+	Global well-posedness for the modified korteweg-de vries equation	1999	German Fonsecal Felipe Linares Gustavo Ponce
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