Journal of Guangxi Normal University(Natural Science Edition) ›› 2024, Vol. 42 ›› Issue (1): 120-127.doi: 10.16088/j.issn.1001-6600.2023032403

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Regularity of Global Attractors for Magnetohydrodynamic Equations

HU Kailun, CHEN Min, LUO Hong*   

  1. School of Mathematical Sciences, Sichuan Normal University, Chengdu Sichuan 610068, China
  • Received:2023-03-24 Revised:2023-05-19 Online:2024-01-25 Published:2024-01-19

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Abstract: 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 H1 and H2 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 Hk for any k≥0, which attracts any bounded set in the Hk-norm.

Key words: magnetohydrodynamic equations, regularity, global attractor, semigroup of operator, iteration method

CLC Number:  O175
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