Stability of hydrostatic equilibrium for the 2D magnetic Bénard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity

Abstract

In mathematics and physics, the problem of the stability of perturbations near the hydrostatic balance is very important. Due to the classical tools designed for the fully dissipated systems are no longer apply, stability and global regularity problems on partially dissipated magnetic Bénard fluid equations can be extremely challenging. This paper considers the stability problem on perturbations near the hydrostatic equilibrium for the 2D magnetic Bénard fluid equations. We establish the global \(H^1\)-stability of the 2D magnetic Bénard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity and affirm the global stability in the Sobolev space \(H^1\) setting.

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Acknowledgements

The author would like to express sincere gratitude to Professor Jiahong Wu for guidance, constant encouragement and providing an excellent research environment. The authors would also like to thank the referee for his/her pertinent comments and advice. This work was partially supported by the National Natural Science Foundation of China (No. 11571243, 11971331), China Scholarship Council(No. 202008515084), Opening Fund of Geomathematics Key Laboratory of Sichuan Province (No. scsxdz2020zd02) and Teacher’s development Scientific Research Staring Foundation of Chengdu University of Technology (No.10912-KYQD2019_07717).

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Correspondence to Liangliang Ma.

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The research of L. Ma was partially supported by the National Natural Science Foundation of China (No. 11571243, 11971331), China Scholarship Council (No. 202008515084), Opening Fund of Geomathematics Key Laboratory of Sichuan Province (No. scsxdz2020zd02) and the Teacher development Scientific Research Staring Foundation of Chengdu University of Technology (No. 10912-KYQD2019_07717).

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Ma, L. Stability of hydrostatic equilibrium for the 2D magnetic Bénard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity. Z. Angew. Math. Phys. 72, 1 (2021). https://doi.org/10.1007/s00033-020-01428-z

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Keywords

  • Magnetic Bénard fluid equations
  • Hydrostatic equilibrium
  • Mixed partial viscosity
  • Stability

Mathematics Subject Classification

  • 35A05
  • 35Q35
  • 76D03