Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation

Zdzislaw Brzezniak, Ben Goldys, Terence Jegaraj

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The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative space-dependent noise is considered for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a sphere $\mathbb S^2$. The regularity of weak solutions is also discussed. Some of the regularity results are new even for the deterministic Landau-Lifshitz-Gilbert equation.
Original languageEnglish
Pages (from-to)1-33
Number of pages33
JournalApplied Mathematics Research eXpress
Issue number1
Early online date1 Apr 2012
Publication statusPublished - Apr 2012

Bibliographical note

Appl Math Res Express first published online April 19, 2012


  • Landau-Lifshitz-Gilbert equation,
  • weak martingale solution,
  • Galerkin approx-imations,
  • compact embedding.

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