In this paper, we investigate the magnetohydrodynamic system with exponential type damping α(e β|u| 2 −1)u. We prove existence of a global in time weak solution and a global in time unique strong solutions, for any α, β ∈ (0, ∞). The proofs are based on energy methods and use compactness argument for the existence results, and Gronwall lemma for the uniqueness. Friedrich approximation and standard techniques are also used.
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