论文标题
驯服的MHD方程
The Tamed MHD Equations
论文作者
论文摘要
我们研究磁性水力学（MHD）方程的正则版本，即驯服MHD（TMHD）方程。它们是通过多孔培养基传导流体流动的模型。我们证明TMHD在整个空间上的存在和独特性$ \ mathbb {r}^{3} $，平滑的数据会引起平滑的解决方案，并表明TMHD的解决方案会收敛到MHD方程的合适弱解决方案，因为taming参数$ n $ n $倾向于Infinity。此外，我们将Navier-Stokes方程的规律性结果调整为MHD案例。
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.
