Self-similar solutions for the Schrödinger map equation

被引：0
|
作者：
Pierre Germain
Jalal Shatah
Chongchun Zeng
机构：
[1] New York University,Courant Institute of Mathematical Sciences
[2] Georgia Institute of Technology,School of Mathematics
来源：
Mathematische Zeitschrift | 2010年 / 264卷
关键词：
Global Existence; Besov Space; Lorentz Space; Real Interpolation; Constant Gaussian Curvature;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study in this article the equivariant Schrödinger map equation in dimension 2, from the Euclidean plane to the sphere. A family of self-similar solutions is constructed; this provides an example of regularity breakdown for the Schrödinger map. These solutions do not have finite energy, and hence do not fit into the usual framework for solutions. For data of infinite energy but small in some norm, we build up associated global solutions.
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页码：697 / 707
页数：10
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