Stability for a system of the 2D magnetohydrodynamic equations with partial dissipation. (English) Zbl 1417.35126
Summary: This paper examines the stability problem on perturbations near a physically important steady state solution of the 2D magnetohydrodynamic (MHD) system with only partial dissipation. We obtain two main results. The first assesses the asymptotic linear stability with explicit decay rates while the second affirms the global stability in the Sobolev space \(H^1\) setting.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 35B35 | Stability in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
background magnetic field; large-time behavior; resistive magnetohydrodynamic equation; stabilityReferences:
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