Open Access
2006 Low-regularity Schrödinger maps
Alexandru D. Ionescu, Carlos E. Kenig
Differential Integral Equations 19(11): 1271-1300 (2006). DOI: 10.57262/die/1356050302


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 $s_0\in H^{{\sigma_0}}_Q(\mathbb{R}^d;\mathbb{S}^2)$, ${\sigma_0}>(d+1)/2$, $Q\in\mathbb{S}^2$.


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Alexandru D. Ionescu. Carlos E. Kenig. "Low-regularity Schrödinger maps." Differential Integral Equations 19 (11) 1271 - 1300, 2006.


Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35449
MathSciNet: MR2278007
Digital Object Identifier: 10.57262/die/1356050302

Primary: 35Q55
Secondary: 35B30

Rights: Copyright © 2006 Khayyam Publishing, Inc.

Vol.19 • No. 11 • 2006
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