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Stabilization Effects of Magnetic Field on a 2D Anisotropic MHD System with Partial Dissipation

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Abstract

To uncover that the magnetic field mechanism can stabilize electrically conducting turbulent fluids, we investigate the stability of a special two dimensional anisotropic MHD system with vertical dissipation in the horizontal velocity component and partial magnetic damping near a background magnetic field. Since the MHD system has only vertical dissipation in the horizontal velocity and vertical magnetic damping, the stability issue and large time behavior problem of the linearized magneto-hydrodynamic system is not trivial. By performing refined energy estimates on the linear system coupled with a careful analysis of the nonlinearities, the stability of a MHD-type system near a background magnetic field is justified for the initial data belonging to \(H^{3}(\mathbf{R}^{2})\) space. The authors also build the explicit decay rates of the linearized system.

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Funding

The authors are partially supported by NNSF of China(NO. 11971209 and 11961032) and the foundation of the Education Division in Jiangxi Province.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, Jiangxi, 330022, P.R. China

    Dongxiang Chen & Fangfang Jian

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  1. Dongxiang Chen
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  2. Fangfang Jian
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Correspondence to Dongxiang Chen.

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Chen, D., Jian, F. Stabilization Effects of Magnetic Field on a 2D Anisotropic MHD System with Partial Dissipation. Acta Appl Math 187, 9 (2023). https://doi.org/10.1007/s10440-023-00602-5

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