To understand that a background magnetic field can smooth and stabilize the electrically conducting turbulent fluids, we focus on some 2D magnetohydrodynamic (MHD) systems with partial dissipation near a background magnetic field in the periodic domain or . This paper shows the stabilization effect of the background magnetic field and the exponential decay of solutions by energy estimate and Poincáre's inequality.
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Li et al. (2026) studied this question.
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