Self-similar solutions for the Schrödinger map equation

Pierre Germain, Jalal Shatah, Chongchun Zeng

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)697-707
Number of pages11
JournalMathematische Zeitschrift
Volume264
Issue number3
DOIs
StatePublished - Jan 2010

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Self-similar Solutions
Equivariant Map
Euclidean plane
Energy
Global Solution
Breakdown
Regularity
Norm
Family
Framework

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Self-similar solutions for the Schrödinger map equation. / Germain, Pierre; Shatah, Jalal; Zeng, Chongchun.

In: Mathematische Zeitschrift, Vol. 264, No. 3, 01.2010, p. 697-707.

Research output: Contribution to journalArticle

Germain, Pierre ; Shatah, Jalal ; Zeng, Chongchun. / Self-similar solutions for the Schrödinger map equation. In: Mathematische Zeitschrift. 2010 ; Vol. 264, No. 3. pp. 697-707.
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