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The stability of localized solutions of Landau‐Lifshitz equations
Author(s) -
Gustafson Stephen,
Shatah Jalal
Publication year - 2002
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3024
Subject(s) - landau–lifshitz–gilbert equation , equivariant map , mathematics , stability (learning theory) , anisotropy , ferromagnetism , class (philosophy) , cauchy problem , mathematical analysis , mathematical physics , initial value problem , pure mathematics , condensed matter physics , physics , quantum mechanics , magnetic field , magnetization , machine learning , artificial intelligence , computer science
We study the Landau‐Lifshitz equation of ferromagnetism on ℝ 2 , 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. © 2002 Wiley Periodicals, Inc.