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arXiv · 0901.0039

Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation

Z. Brzezniak·B. Goldys
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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 $\mathbb S^2$. The regularity of weak solutions is also discussed. Some of the regularity results are new even for the deterministic Landau-Lifshitz-Gilbert equation.

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Z. Brzezniak, B. Goldys. 2008-12-31. Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation. https://arxiv.org/abs/0901.0039

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