Analytical Study of a 3D-MHD System with Exponential Damping

R. Selmi; A. Sboui; J. Benameur

doi:10.26713/cma.v13i3.1826

Authors

R. Selmi Department of Mathematics, College of Science, Northern Border University, P.O. Box 1321, Arar, 73222, KSA; University of Gabes, Faculty of Science of Gabes, Department of Mathematics, Gabes 6072, Tunisia; University of Tunis El Manar, Faculty of Science of Tunis, Laboratory of Partial Differential Equations and Applications (LR03ES04), Tunis, 1068, Tunisia https://orcid.org/0000-0003-3010-3732 (unauthenticated)
A. Sboui Department of Mathematics, Faculty of Science and Art (TURAIF), Northern Border University, KSA; University of Tunis El Manar, Faculty of Science of Tunis, Laboratory of Partial Differential Equations and Applications (LR03ES04), Tunis, 1068, Tunisia; University of Carthage, ISSATM, Department of Mathematics, Tunisia https://orcid.org/0000-0002-1822-8906 (unauthenticated)
J. Benameur University of Gabes, Faculty of Science of Gabes, Department of Mathematics, Gabes 6072, Tunisia https://orcid.org/0000-0002-6043-9037 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v13i3.1826

Keywords:

Magnetohydrodynamic system, Exponential damping, Existence, Uniqueness, Weak solution, Strong solution, Global solution

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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References

H. Bahouri, J.-Y. Chemin and R. Danchin, Fourier analysis and nonlinear partial differential equations, in: Grundlehren der mathematischen Wissenschaften (GL, Vol. 343), Springer-Verlag, (2011), DOI: 10.1007/978-3-642-16830-7.

J. Benameur, Global weak solution of 3D-NSE with exponential damping, Open Mathematics 20(1) (2022), 590 – 607, DOI: 10.1515/math-2022-0050.

M. Blel and J. Benameur, Long-time decay of leray solution of 3d-nse with exponential damping, Fractals 2240236, DOI: 10.1142/S0218348X22402368

A. Chaabani, R. Nasfi, R. Selmi and M. Zaabi, Well-posedness and convergence results for strong solution to a 3D-regularized Boussinesq system, Mathematical Methods in the Applied Sciences, (2016), published: 14 April 2016, DOI: 10.1002/mma.3950.

M. Sermange and R. Temam, Some mathematical questions related to the mhd equations, Communications on Pure and Applied Mathematics 36(5) (1983), 635 – 664, DOI: 10.1002/cpa.3160360506.