Abstract
In this paper, we investigate the magnetohydrodynamic system with exponential type damping \(\alpha (e^{\beta |u|^2}-1)u\). We prove existence of a global in time weak solution and a global in time unique strong solutions, for any \(\alpha,\beta\in(0,\infty)\). 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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