The Stability of Localized Solutions of Landau-Lifshitz Equations

Stephen Gustafson, Jalal Shatah

Research output: Contribution to journalArticle

Abstract

We study the Landau-Lifshitz equation of ferromagnetism on R2, with an easy-axis anisotropy. We establish the existence of topologically nontrivial, periodic solutions, and show they are stable against equivariant perturbations. Along the way, we establish the global well-posedness of the Cauchy problem for a class of data with no size restriction.

Original languageEnglish (US)
Pages (from-to)1136-1159
Number of pages24
JournalCommunications on Pure and Applied Mathematics
Volume55
Issue number9
DOIs
StatePublished - Sep 2002

Fingerprint

Landau-Lifshitz Equation
Ferromagnetism
Anisotropy
Global Well-posedness
Equivariant
Cauchy Problem
Periodic Solution
Restriction
Perturbation
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

The Stability of Localized Solutions of Landau-Lifshitz Equations. / Gustafson, Stephen; Shatah, Jalal.

In: Communications on Pure and Applied Mathematics, Vol. 55, No. 9, 09.2002, p. 1136-1159.

Research output: Contribution to journalArticle

Gustafson, Stephen ; Shatah, Jalal. / The Stability of Localized Solutions of Landau-Lifshitz Equations. In: Communications on Pure and Applied Mathematics. 2002 ; Vol. 55, No. 9. pp. 1136-1159.
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