Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation

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

2008-12-31

arxiv.org/abs/0901.0039v1

Mathematics

Probability

Scientific paper

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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