The Tamed MHD Equations

Andre Schenke

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arXiv · 2003.06084

The Tamed MHD Equations

Andre Schenke

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Abstract

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 $\mathbb{R}^{3}$, 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.

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Andre Schenke. 2020-03-13. The Tamed MHD Equations. https://arxiv.org/abs/2003.06084

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