This paper deals with the existence of global weak solutions for 3D MHD equations when the initial data belong to the weighted spaces \(L^2_{w_\gamma }\), with \(w_\gamma (x)=(1+\vert x\vert )^{-\gamma }\) and \(0 \le \gamma \le 2\). Moreover, we prove the existence of discretely self-similar solutions for 3D MHD equations for discretely self-similar initial data which are locally square integrable. Our methods are inspired of a recent work (Fernández-Dalgo et al. in Arch Rational Mech Anal 237:347–382, 2020) for the Navier–Stokes equations.

中文翻译：

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加权$$ L ^ 2 $$ L 2空间中3D MHD方程的离散自相似解和全局弱解

当初始数据属于加权空间\（L ^ 2_ {w_ \ gamma} \）且\（w_ \ gamma（x）=（1+ \ ）时，本文讨论了3D MHD方程全局弱解的存在vert x \ vert）^ {-\ gamma} \）和\（0 \ le \ gamma \ le 2 \）。此外，我们证明了离散自相似初始数据的3D MHD方程的离散自相似解的存在性，这些局部数据是局部平方可积的。我们的方法的灵感来自Navier-Stokes方程的最新工作（Fernández-Dalgo等人，Arch Rational Mech Anal 237：347–382，2020）。