Weak solutions of the Stochastic Landau–Lifshitz–Gilbert Equations with nonzero anisotrophy energy

Abstract

We study a stochastic Landau-Lifschitz-Gilbert Equations with non-zero anisotrophy energy and multidimensional noise. We prove the existence and some regularities of weak solution proved. Our paper is motivated by finite-dimensional study of stochastic LLGEs or general stochasric differential equations with constraints studied by Kohn et al \cite{Kohn_2005} and Leli{\`e}vre et al \cite{LeBris_2008}.