<p>This paper considers the stochastic Landau-Lifshitz-Baryakhtar (SLLBar, for short) equation with pure jump noise in the Marcus canonical form, which describes the dynamics of the magnetic spin field in a ferromagnet at elevated temperatures, with the effective field <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\textbf{H}_{\text {eff}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="bold">H</mi> <mtext>eff</mtext> </msub> </math></EquationSource> </InlineEquation> influenced by external random noise. Under the natural assumption that the magnetic body <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathcal {O}\subset \mathbb {R}^d$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">O</mi> <mo>⊂</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$d=1,2,3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>) is bounded with smooth boundary, we prove that the initial-boundary value problem of the SLLBar equation admits a unique global probabilistically strong and analytically weak solution for initial data in the energy space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mathbb {H}^1$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation>. Furthermore, by employing the weak convergence method, we establish a Freidlin–Wentzell type large deviation principle for pathwise solutions to the SLLBar equation.</p>

Well-posedness and Large Deviations of Lévy-driven Marcus Stochastic Landau-Lifshitz-Baryakhtar Equation

期刊论文
发表日期：

2026年1月24日

查看全文

Fan Xu,
Bin Liu,
Lei Zhang

摘要

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