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Stability for a system of 2D incompressible anisotropic magnetohydrodynamic equations

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Abstract

This paper investigates the global well-posedness and the stability of perturbations near a background magnetic field on the 2D incompressible anisotropic magnetohydrodynamic equations. More precisely, we consider the system with partial mixed velocity dissipations and horizontal magnetic diffusion. Two goals are achieved. First, we obtain the global well-posedness and the \(H^2\)-stability for the nonlinear MHD equations. The approach is to apply the bootstrapping argument. Efforts are devoted to the a priori estimate of a energy functional. Second, we establish the long-time behavior of explicit decay rates of the solution in homogeneous Sobolev spaces \(\dot{H}^s\) for the linear system under the suitable assumptions for the initial data. Our work proves that any perturbations near a background magnetic field remain asymptotically stable.

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Acknowledgements

Lin was partially supported by the National Natural Science Foundation of China NSFC under Grant 11701049, the Natural Science Foundation of SiChuan Province under Grant 2023NSFSC0056 and the China Postdoctoral Science Foundation under Grant 2017M622989.

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Authors and Affiliations

  1. Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu, 610059, People’s Republic of China

    Hongxia Lin, Tiantian Chen, Ru Bai & Heng Zhang

  2. College of Mathematics and Physics, Chengdu University of Technology, Chengdu, 610059, People’s Republic of China

    Hongxia Lin, Tiantian Chen, Ru Bai & Heng Zhang

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  1. Hongxia Lin
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Lin, H., Chen, T., Bai, R. et al. Stability for a system of 2D incompressible anisotropic magnetohydrodynamic equations. Z. Angew. Math. Phys. 74, 53 (2023). https://doi.org/10.1007/s00033-023-01944-8

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