Communications in Mathematical Sciences

Volume 18 (2020)

Number 3

On the smooth solutions of Landau–Lifshitz–Bloch equations of antiferromagnets

Pages: 837 – 849



Yu-Feng Wang (College of Science, Minzu University of China, Beijing, China)

Bo-Ling Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Ming Zeng (College of Applied Sciences, Beijing University of Technology, Beijing, China)


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.


smooth solutions, Landau–Lifshitz–Bloch equation

2010 Mathematics Subject Classification

35A01, 35A02, 35B65

This work has been supported by the National Natural Science Foundation of China (Grant No. 11571254 and 11801597).

Received 26 August 2018

Accepted 6 December 2019

Published 30 June 2020