Abstract
The existence of global attractors is proved for the MHD equations with damping terms |u|α−1u and |B|β−1B(α,β⩾1) on a bounded domain Ω⊂R3. First we establish the well-posedness of strong solutions. Then, the continuity of the corresponding semigroup is verified under the assumption α,β<5, which is guided by Gagliardo-Nirenberg inequality. Finally, the system is shown to possess an (V,V)-global attractor and an (V,H2)-global attractor.
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