The Stability of Localized Solutions of Landau-Lifshitz Equations

Stephen Gustafson; Jalal Shatah

doi:10.1002/cpa.3024

The Stability of Localized Solutions of Landau-Lifshitz Equations

Stephen Gustafson, Jalal Shatah

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1136-1159
Number of pages	24
Journal	Communications on Pure and Applied Mathematics
Volume	55
Issue number	9
DOIs	https://doi.org/10.1002/cpa.3024
State	Published - Sep 2002

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/cpa.3024

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title = "The Stability of Localized Solutions of Landau-Lifshitz Equations",

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.",

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AB - 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.

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The Stability of Localized Solutions of Landau-Lifshitz Equations

Abstract

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