Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation

2008/12/31 by Brzezniak, Z., Goldys, B.
#35K55 #35Q40 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0901.0039

Abstract

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 S². The regularity of weak solutions is also discussed. Some of the regularity results are new even for the deterministic Landau-Lifshitz-Gilbert equation.

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