Differential and Integral Equations

Weak continuity of dynamical systems for the KdV and mKdV equations

Shangbin Cui and Carlos E. Kenig

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Differential Integral Equations, Volume 23, Number 11/12 (2010), 1001-1022.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019070

Mathematical Reviews number (MathSciNet)
MR2742475

Zentralblatt MATH identifier
1240.35448

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Citation

Cui, Shangbin; Kenig, Carlos E. Weak continuity of dynamical systems for the KdV and mKdV equations. Differential Integral Equations 23 (2010), no. 11/12, 1001--1022. https://projecteuclid.org/euclid.die/1356019070


Export citation