Open Access
Translator Disclaimer
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


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.


Download Citation

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.


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

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

Primary: 35Q53

Rights: Copyright © 2010 Khayyam Publishing, Inc.


Vol.23 • No. 11/12 • November/December 2010
Back to Top