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December 2019, 11(4): 621-637. doi: 10.3934/jgm.2019031
Global well-posedness of a 3D MHD model in porous media
Edriss S. Titi 1,2,, and Saber Trabelsi 3,
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Department of Mathematics, Texas A & M University College Station, 3368 TAMU, College Station, TX 77843-3368, USA
Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, KSA
This work is dedicated to Professor Darryl Holm on the occasion of his 70th birthday
Received May 2018 Revised March 2019 Published November 2019
In this paper we show the global well-posedness of solutions to a three-dimensional magnetohydrodynamical (MHD) model in porous media. Compared to the classical MHD equations, our system involves a nonlinear damping term in the momentum equations due to the "Brinkman-Forcheimer-extended-Darcy" law of flow in porous media.
Keywords: Magneto-hydrodynamics, porous media, Brinkman-Forchheimer-extended-Darcy model, 3D Navier-Stokes equations.
Mathematics Subject Classification: 76W05, 76S05, 35Q30, 35Q35, 76B03, 93C10, 93C20, 76B75.
Citation: Edriss S. Titi, Saber Trabelsi. Global well-posedness of a 3D MHD model in porous media. Journal of Geometric Mechanics, 2019, 11 (4) : 621-637. doi: 10.3934/jgm.2019031
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Edriss S. Titi Saber Trabelsi