Differential and Integral Equations

Low-regularity Schrödinger maps

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