The tamed MHD equations

We study a regularised version of the magnetohydrodynamics (MHD) equations, the tamed MHD (TMHD) equations. They are a model for the flow of electrically conducting fluids through porous media. We prove existence and uniqueness of TMHD on the whole space R 3 , that smooth data give rise to smooth solutions and show that solutions to TMHD converge to a suitable weak solution of the MHD equations as the taming parameter N tends to infinity. Furthermore, we adapt a regularity result for the Navier–Stokes equations to the MHD case.