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Stochastic Landau–Lifshitz–Bloch Equation with Transport Noise: Well-Posedness, Dissipation Enhancement

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Abstract

The Landau–Lifshitz–Bloch equation is the only valid model describing the simulation of heat-assisted magnetic recording around the Curie temperature. In order to explain the noise-induced phenomenon more comprehensively between different equilibrium states, we consider a special type of noise: multiplicative transport noise, to perturb the equation on a torus \({\mathbb {T}}^d, d=2,3\). The existence of martingale weak solution is proved for \(d=2,3\). For \(d=2\), we show the uniqueness, then the strong pathwise solution is established. Compared with other type of Wiener noise, we further show that the transport noise provides the regularizing effect, thus, the energy dissipation is enhanced.

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Acknowledgements

The authors would like to thank the anonymous referees for their very valuable suggestions and constructive comments. C. Sun is supported by the National Natural Science Foundation of China (Grant No. 11701269) and the National Science Foundation of Jiangsu Province (Grant No. BK20231301).

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  1. School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, 210046, China

    Zhaoyang Qiu & Chengfeng Sun

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  1. Zhaoyang Qiu
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Correspondence to Zhaoyang Qiu.

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Communicated by Li-Cheng Tsai.

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Qiu, Z., Sun, C. Stochastic Landau–Lifshitz–Bloch Equation with Transport Noise: Well-Posedness, Dissipation Enhancement. J Stat Phys 191, 43 (2024). https://doi.org/10.1007/s10955-024-03259-y

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