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May/June 2009 Well-posedness of the Cauchy problem for the Korteweg-de Vries equation at the critical regularity
Nobu Kishimoto
Differential Integral Equations 22(5/6): 447-464 (May/June 2009).

Abstract

The Cauchy problem for the nonperiodic KdV equation is shown by the iteration method to be locally well-posed in $H^{-3/4}(\mathbb R )$. In particular, solutions are unique in the whole Banach space for the iteration. This extends the previous well-posedness result in $H^s$, $s>-3/4$ obtained by Kenig, Ponce and Vega (1996) to the limiting case, and improves the existence result in $H^{-3/4}$ given by Christ, Colliander and Tao (2003). Our result immediately yields global well-posedness for the KdV equation in $H^{-3/4}(\mathbb R )$ and for the modified KdV equation in $H^{1/4}(\mathbb R )$, combined with the argument of Colliander, Keel, Staffilani, Takaoka and Tao (2003).

Citation

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Nobu Kishimoto. "Well-posedness of the Cauchy problem for the Korteweg-de Vries equation at the critical regularity." Differential Integral Equations 22 (5/6) 447 - 464, May/June 2009.

Information

Published: May/June 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35461
MathSciNet: MR2501679

Subjects:
Primary: 35Q53
Secondary: 35B30

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.22 • No. 5/6 • May/June 2009
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