THE ENERGY CONSERVATION OF THE LANDAU-LIFSHITZ-BLOCH EQUATION  

作　　者：许秋菊 王华桥 Qiuju XU;Huaqiao WANG(School of Mathematical Sciences,Chongqing Normal University,Chongqing 400047,China;College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China)

机构地区：[1]School of Mathematical Sciences,Chongqing Normal University,Chongqing 400047,China [2]College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China

出　　处：《Acta Mathematica Scientia》2023年第4期1841-1851,共11页数学物理学报（B辑英文版）

基　　金：the National Natural Science Foundation of China (11901070);the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202100523);the Research Project of Chongqing Education Commission(CXQT21014);the Open Project of Key Laboratory,School of Mathematical Sciences,Chongqing Normal University (CSSXKFKTZ202005);the National Natural Science Foundation of China (11901066);the Natural Science Foundation of Chongqing (cstc2019jcyj-msxm X0167);the Fundamental Research Funds for the Central Universities (2022CDJXY-001, 2020CDJQY-A040)。

摘　　要：In this paper,we consider the three-dimensional Landau-Lifshitz-Bloch equation in the whole space,which can describe the micromagnetic dynamic behavior of material at all temperatures,especially near the Curie temperature.We establish a sufficient condition of energy conservation for when weak solutions of the Landau-Lifshitz-Bloch equation with the temperature higher than the Curie temperature and its gradient belong to the Besov space L_(loc)^(3);B_(p,c0)^(α)(R^(3)))for some α∈(1/2,1)and p=9/(3α+1).Moreover,we also use the dimensional homogeneity to explain that the restrictions on the indicators are reasonable.

关 键 词：Landau-Lifshitz-Bloch equation weak solutions energy conservation 

分 类 号：O411[理学—理论物理]