Global well-posedness of a 3D MHD model in porous media

Titi Edriss S.; Trabelsi Saber

doi:10.3934/jgm.2019031

Article Contents

2019, Volume 11, Issue 4: 621-637. Doi: 10.3934/jgm.2019031

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Global well-posedness of a 3D MHD model in porous media

Titi Edriss S.^1,2, , and
Trabelsi Saber^3,

1.
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
2.
Department of Mathematics, Texas A & M University College Station, 3368 TAMU, College Station, TX 77843-3368, USA
3.
Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, KSA

^* Corresponding author
^* Corresponding author

This work is dedicated to Professor Darryl Holm on the occasion of his 70^th birthday

Received: May 1, 2018

Revised: March 1, 2019

Published online: November 30, 2019

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Abstract

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.

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