Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation

TY - JOUR

T1 - Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation

AU - Brzezniak, Zdzislaw

AU - Goldys, Ben

AU - Jegaraj, Terence

N1 - Appl Math Res Express first published online April 19, 2012

PY - 2012/4

Y1 - 2012/4

N2 - 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.

AB - 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.

KW - Landau-Lifshitz-Gilbert equation,

KW - weak martingale solution,

KW - Galerkin approx-imations,

KW - compact embedding.

UR - http://www.scopus.com/inward/record.url?scp=84874891062&partnerID=8YFLogxK

U2 - 10.1093/amrx/abs009

DO - 10.1093/amrx/abs009

M3 - Article

SN - 1687-1200

VL - 2013

SP - 1

EP - 33

JO - Applied Mathematics Research eXpress

JF - Applied Mathematics Research eXpress

IS - 1

ER -