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2007 A remark on global well-posedness below $L^2$ for the GKDV-3 equation
Axel Grünrock, Mahendra Panthee, Jorge Drumond Silva
Differential Integral Equations 20(11): 1229-1236 (2007).

Abstract

The $I$-method in its first version as developed by Colliander et~al. in [2] is applied to prove that the Cauchy-problem for the generalized Korteweg-de Vries equation of order three (gKdV-3) is globally well-posed for large real-valued data in the Sobolev space $H^s(\mathbb R \rightarrow \mathbb R)$, provided $s>-\frac{1}{42}$.

Citation

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Axel Grünrock. Mahendra Panthee. Jorge Drumond Silva. "A remark on global well-posedness below $L^2$ for the GKDV-3 equation." Differential Integral Equations 20 (11) 1229 - 1236, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35413
MathSciNet: MR2372424

Subjects:
Primary: 35Q53
Secondary: 35B30 , 35B65

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 11 • 2007
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