November/December 2010 Weak continuity of dynamical systems for the KdV and mKdV equations
Shangbin Cui, Carlos E. Kenig
Differential Integral Equations 23(11/12): 1001-1022 (November/December 2010). DOI: 10.57262/die/1356019070

Abstract

In this paper we study weak continuity of the dynamical systems for the KdV equation in $H^{-3/4}(\mathbb{R})$ and the modified KdV equation in $H^{1/4}(\mathbb{R})$. This topic should have significant applications in the study of other properties of these equations such as finite time blow-up and asymptotic stability and instability of solitary waves. The spaces considered here are borderline Sobolev spaces for the corresponding equations from the viewpoint of the local well-posedness theory. We first use a variant of the method of [5] to prove weak continuity for the mKdV, and next use a similar result for an mKdV system and the generalized Miura transform to get weak continuity for the KdV equation.

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Shangbin Cui. Carlos E. Kenig. "Weak continuity of dynamical systems for the KdV and mKdV equations." Differential Integral Equations 23 (11/12) 1001 - 1022, November/December 2010. https://doi.org/10.57262/die/1356019070

Information

Published: November/December 2010
First available in Project Euclid: 20 December 2012

MathSciNet: MR2742475
zbMATH: 1240.35448
Digital Object Identifier: 10.57262/die/1356019070

Subjects:
Primary: 35Q53

Rights: Copyright © 2010 Khayyam Publishing, Inc.

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Vol.23 • No. 11/12 • November/December 2010
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