Communications in Mathematics and Applications Vol. 13, No. 3, pp. 935–942, 2022 ISSN 0975-8607 (online); 0976-5905 (print) Published by RGN Publications http://www.rgnpublications.com DOI: 10.26713/cma.v13i3.1826 Research Article Analytical Study of a 3D-MHD System with Exponential Damping R. Selmi* 1,3,4 , A. Sboui 2,4,5 and J. Benameur 3 1 Department of Mathematics, College of Science, Northern Border University, P.O. Box 1321, Arar, 73222, KSA 2 Department of Mathematics, Faculty of Science and Art (TURAIF), Northern Border University, KSA 3 University of Gabes, Faculty of Science of Gabes, Department of Mathematics, Gabes 6072, Tunisia 4 University of Tunis El Manar, Faculty of Science of Tunis, Laboratory of Partial Differential Equations and Applications (LR03ES04), Tunis, 1068, Tunisia 5 University of Carthage, ISSATM, Department of Mathematics, Tunisia *Corresponding author: ridha.selmi@nbu.edu.sa Received: February 16, 2022 Accepted: March 3, 2022 Abstract. 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. Keywords. Magnetohydrodynamic system, Exponential damping, Existence, Uniqueness, Weak solution, Strong solution, Global solution Mathematics Subject Classification (2020). 35A01, 35A02, 35B45. Copyright © 2022 R. Selmi, A. Sboui and J. Benameur. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction In this paper, we study the following magnetohydrodynamic system with exponential damping: (S)            ∂ t u − ∆u + u ·∇u + b ·∇b + α( e β|u| 2 − 1) u = −∇ p, in R + × R 3 , ∂ t b − ∆b + b ·∇u − u ·∇b = 0, in R + × R 3 , div u = 0, div b = 0, in R + × R 3 , u(0, x) = u 0 ( x), b(0, x) = b 0 ( x), in R 3 ,