In this paper, we investigate the smooth solutions for the antiferromagnets Landau–Lifshitz–Bloch (LLB) equation with periodic initial value, which can describe the dynamics of micromagnets under high temperature. The existence and uniqueness of smooth solutions for LLB equation in $\mathbb{R}^2$ and $\mathbb{R}^3$ are proved.

中文翻译：

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关于反铁磁体的Landau-Lifshitz-Bloch方程的光滑解

在本文中，我们研究了具有周期性初始值的反铁磁体Landau–Lifshitz–Bloch（LLB）方程的光滑解，该方程可描述高温下微磁体的动力学。证明了$ \ mathbb {R} ^ 2 $和$ \ mathbb {R} ^ 3 $中LLB方程光滑解的存在性和唯一性。