您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (5): 56-66.doi: 10.6040/j.issn.1671-9352.0.2023.416

• • 上一篇    

一类具有磁阻尼项的磁流体动力学方程的全局吸引子

吴辰龙,刘瑞宽*,亓子成   

  1. 西南石油大学理学院, 四川 成都 610500
  • 发布日期:2025-05-19
  • 通讯作者: 刘瑞宽(1989— ),男,讲师,硕士生导师,博士,研究方向为非线性微分方程及其应用. E-mali:liuruikuan2008@163.com
  • 作者简介:吴辰龙(1998— ),男,硕士研究生,研究方向为偏微分方程适定性问题. E-mali:wuchenlong9810@163.com*通信作者:刘瑞宽(1989— ),男,讲师,硕士生导师,博士,研究方向为非线性微分方程及其应用. E-mali:liuruikuan2008@163.com
  • 基金资助:
    四川省自然科学基金资助项目(2022NSFSC0529);南充市-西南石油大学市校科技战略合作专项资金资助项目(23XNSYJG0005)

Global attractors for a class of magneto-hydrodynamic equations with magnetic damping terms

WU Chenlong, LIU Ruikuan*, QI Zicheng   

  1. School of Science, Southwest Petroleum University, Chengdu 610500, Sichuan, China
  • Published:2025-05-19

PDF (PC)

35

摘要： 讨论了一类具有磁阻尼项的二维不可压缩磁流体动力学模型解的长时间渐近行为,证明了有界吸收集的存在性,利用 C-条件方法,得到了该模型在具有较高正则性的相空间上全局吸引子的存在性。

关键词: 磁流体动力学, 磁阻尼项, C-条件, 全局吸引子

Abstract: The long time asymptotic behavior of solutions of a class of two dimensional incompressible magnetohydrodynamic equations with magnetic damping term is discussed. By proving the existence of the bounded absorbing set and using the C-condition method, the existence of the global attractors on the phase space with higher regularity is obtained.

Key words: magneto-hydrodynamics, magnetic damping term, the C-condition, global attractors

中图分类号: 

  • O175.29
[1] LIU Ruikan, YANG Jiayan. Magneto-hydrodynamical model for plasma[J]. Zeitschrift für angewandte Mathematik und Physik, 2017, 68:1-15.
[2] LIU Ruikuan, YANG Jiayan. Global strong solutions of a 2D new magnetohydrodynamic system[J]. Applications of Mathematics, 2020, 65(1):105-120.
[3] TEMAM R. Infinite-dimensional dynamical systems in mechanics and physics[M]. New York: Springer, 1997.
[4] LUKASZEWICZ G. Long time behavior of 2D micropolar fluid flows[J]. Mathematical and Computer Modelling, 2001, 34(5/6):487-509.
[5] MA Qingfeng, WANG Shouhong, ZHONG Chengkui. Necessary and sufficient conditions for the existence of global attractors for semigroups and applications[J]. Indiana University Mathematics Journal, 2001, 51(6):1541-1559.
[6] LU Songsong, WU Hongqing, ZHONG Chengkui. Attractors for non-autonomous 2D Navier-Stokes equations with normal external force[J]. Discrete and Continuous Dynamical Systems, 2005, 13(3):701.
[7] ZHONG Chengkui, YANG Meihua, SUN Chunyou. The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equation[J]. Journal of Differential Equations, 2006, 223(2):367-399.
[8] 马天,汪守宏. 非线性演化方程的稳定性与分歧[M]. 北京:科学出版社,2007. MA Tian, WANG Shouhong. Stability and bifurcation of nonlinear evolution equations[M]. Beijing: Science Press, 2007.
[9] CHEN Jiawen, CHEN Zhimin, DONG Boqing. Existence of H2-global attractors of two-dimensional micropolar fluid flows[J]. Journal of Mathematical Analysis and Applications, 2006, 322(2):512-522.
[10] KLOEDEN P E, LANGA J A. Flattening, squeezing and the existence of random attractors[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2007, 463(2077):163-181.
[11] CARVALHO A, LANGA J A, ROBINSON J. Attractors for infinite-dimensional non-autonomous dynamical systems[M]. Berlin: Springer, 2012.
[12] GARCÍA LUENGO J M, MARÍN RUBIO P, REAL ANGUAS J, et al. Pullback attractors for the non-autonomous 2D Navier-Stokes equations for minimally regularforcing[J]. Discrete and Continuous Dynamical Systems(Series A), 2014, 34(1):203-227.
[13] SUN Wenlong, LI Yeping. Pullback dynamical behaviors of the non-autonomous micropolar fluid flows with minimally regular force and moment[J]. Communications in Mathematical Sciences, 2018, 16(4):1043-1065.
[14] ANH C, SON D. Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains[J]. Annales Polonici Mathematici, 2015, 113(2):129-154.
[15] SONG Xiaoya, XIONG Yangmin. Pullback attractors for 2D MHD equations with delays[J]. Journal of Mathematical Physics, 2021, 62(7):1-29.
[16] SONG Xiaoya. Pullback attractors for 3D MHD equations with damping[J]. Zeitschrift für angewandte Mathematik und Physik, 2022, 73(2):1-16.
[17] CAO Daomin, SONG Xiaoya, SUN Chunyou. Pullback attractors for 2D MHD equations on time-varying domains[J]. Discrete & Continuous Dynamical Systems(Series A), 2022, 42(2):643-677.
[1] 张盈,刘强强,马巧珍. 带记忆的基尔霍夫型梁方程的全局吸引子[J]. 《山东大学学报(理学版)》, 2022, 57(4): 66-75.
[2] 梁霄, 王林山 . 一类S分布时滞递归神经网络的全局吸引子[J]. J4, 2009, 44(4): 57-60 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发