Weak solutions to the equations of stationary magnetohydrodynamic flows in porous media
Youcef Amirat, Laurent Chupin, Rachid St. Touzani · Communications on Pure & Applied Analysis · 2014
We study the differential system which describes the steady flow of an electrically conducting fluid in a saturated porous medium, when the fluid is subjected to the action of a magnetic field. The system consists of the stationary Brinkman-Forchheimer equations and the stationary magnetic induction equation. We prove existence of weak solutions to the system posed in a bounded domain of $\mathbb{R}^3$ and equipped with boundary conditions. We also prove uniqueness in the class of small solutions, and regularity of weak solutions. Then we establish a convergence result, as the Brinkman coefficient (viscosity) tends to 0, of the weak solutions to a solution of the system formed by the Darcy-Forchheimer equations and the magnetic induction equation.