Analytical Study of a 3D-MHD System with Exponential Damping - Selmi, R.; Sboui, A.; Benameur, J. (Communications in Mathematics and Applications, 2022)
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.