Well-posedness and large deviations of L\'{e}vy-driven Marcus stochastic Landau-Lifshitz-Baryakhtar equation

TL;DR

This paper proves the well-posedness and establishes a large deviation principle for solutions of a stochastic Landau-Lifshitz-Baryakhtar equation driven by jump noise, modeling magnetic spin dynamics at elevated temperatures.

Contribution

It provides the first rigorous proof of existence, uniqueness, and large deviations for the SLLBar equation with pure jump noise in Marcus form.

Findings

Existence of unique global solutions in the energy space.

Proof of a Freidlin-Wentzell type large deviation principle.

Application to magnetic spin dynamics under stochastic influences.

Abstract

This paper considers the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with pure jump noise in Marcus canonical form, which describes the dynamics of magnetic spin field in a ferromagnet at elevated temperatures with the effective field $\mathbf{H}_{\textrm{eff}}$ influenced by external random noise. Under the natural assumption that the magnetic body $\mathcal{O}\subset\mathbb{R}^d$ ($d=1,2,3$) is bounded with smooth boundary, we shall prove that the initial-boundary value problem of SLLBar equation possesses a unique global probabilistically strong and analytically weak solution with initial data in the energy space $\mathbb{H}^1(\mathcal{O})$. Then by employing the weak convergence method, we proceed to establish a Freidlin-Wentzell type large deviation principle for pathwise solutions to the SLLBar equation.