磁流体方程全局吸引子的正则性  

Regularity of Global Attractors for Magnetohydrodynamic Equations

作　　者：胡凯伦 陈敏 罗宏 HU Kailun;CHEN Min;LUO Hong(School of Mathematical Sciences,Sichuan Normal University,Chengdu Sichuan 610068,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610068

出　　处：《广西师范大学学报（自然科学版）》2024年第1期120-127,共8页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(12171343);四川省科技厅科研基金(22CXTD0029)。

摘　　要：本文考虑磁流体方程的长时间行为,研究其全局吸引子的正则性。首先,利用分数次空间的嵌入定理和全局吸引子的存在性定理分别得到该方程在空间H 1和H 2中存在全局吸引子;然后,利用迭代方法、线性算子半群的正则性理论和全局吸引子的存在性定理,证明该方程在任意Sobolev空间H^(k)(其中k≥0)中存在全局吸引子,并以H^(k)-范数吸引空间H^(k)中的任意有界集。In this paper,the large time behavior of the solutions to magnetohydrodynamic equations is investigated,focusing on the regularity of the global attractor.Using the embedding theorem of fractional order spaces and the existence theorem of global attractor,it is obtained that the magnetohydrodynamic equations have global attractors in H 1 and H 2 spaces,respectively.Furthermore,by using an iteration method,regularity estimates for the linear operator semigroup and existence theorem of global attractor,it is proved that the magnetohydrodynamic equations have a global attractor in H^(k)for any k≥0,which attracts any bounded set in the H^(k)-norm.

关 键 词：磁流体方程 正则性 全局吸引子 算子半群 迭代方法 

分 类 号：O175[理学—数学]