$L^2 $- DECAY OF SOLUTIONS OF THREE DIMENSIONAL INCOMPRESSIBLE MHD EQUATIONS: A MODIFIED APPROACH
Résumé
In this paper, we adopt a recent and modified approach to prove $L^2$-decay properties of solutions of incompressible MHD equations following the methods in H. Sohr [“{\it The Navier-Stokes Equations: An Elementary Functional Analytic Approach}”, Birkhauser Advanced Texts, Birkhauser Verlag, Basel, 2001. ]
and Duong and Khai [TNU Journal of Science and Technology, Vol. 225 (02), 45-51 (2020) ]. Also, we compare our results with previously known results in the literature and find that our results (decay rate) are sharper than previously proven results. Last Theorem is an additional property of solutions of MHD equations, namely that they approach solution of homogeneous system as $t \to \infty$.
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