Differential and Integral Equations

Low-regularity Schrödinger maps

Alexandru D. Ionescu 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

We prove that the Schrödinger map initial-value problem \begin{equation*} \begin{cases} & \partial_ts=s\times\Delta_x s\,\text{ on }\,\mathbb{R}^d\times[-1,1];\\ & s(0)=s_0 \end{cases} \end{equation*} is locally well posed for small data $s_0\in H^{{\sigma_0}}_Q(\mathbb{R}^d;\mathbb{S}^2)$, ${\sigma_0}>(d+1)/2$, $Q\in\mathbb{S}^2$.

Article information

Source
Differential Integral Equations, Volume 19, Number 11 (2006), 1271-1300.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050302

Mathematical Reviews number (MathSciNet)
MR2278007

Zentralblatt MATH identifier
1212.35449

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

Citation

Ionescu, Alexandru D.; Kenig, Carlos E. Low-regularity Schrödinger maps. Differential Integral Equations 19 (2006), no. 11, 1271--1300. https://projecteuclid.org/euclid.die/1356050302


Export citation