Abstract
The stability problem for the magnetohydrodynamic equations with partial or no dissipation has evoked a considerable interest in recent years. In this paper, we establish the stability near magnetic hydrostatic equilibrium to the three-dimensional magnetic Bénard fluid equations with the mixed partial dissipation involving viscosity, resistivity and heat conduction. Moreover, we obtain the large-time behavior of the corresponding linearized system. Our result mathematically verifies the stabilization of a background magnetic field on the three-dimensional magnetic Bénard fluid.
Citation
Yajie Zhang. Jialiang Wang. Jiang Han. "STABILITY NEAR HYDROSTATIC EQUILIBRIUM TO THE THREE-DIMENSIONAL MAGNETIC BÉNARD FLUID EQUATIONS WITH PARTIAL DISSIPATION." Rocky Mountain J. Math. 53 (3) 983 - 1000, June 2023. https://doi.org/10.1216/rmj.2023.53.983
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