Discretely self-similar solutions for 3D MHD equations and global weak solutions in weighted \(L^2\) spaces
This is a study of global-in-time weak solutions to the magnetohydrodynamics equations in \({\mathbb R}^3\) motivated by a recent approach to the Navier-Stokes equations involving new local energy control in [\textit{P. G. Fernández-Dalgo} and \textit{P. G. Lemarié-Rieusset}, Arch. Ration. Mech. Anal. 237, No. 1, 347--382 (2020; Zbl 1434.35050)]. Initial data in \(L^2((1+|x|)^{-\gamma}\,\mathrm{d}x)\) space (\(0<\gamma\le 2\)) may have infinite energy. Discretely self-similar solutions can be also constructed with the application of this method.
scientific article; zbMATH DE number 7312805
scientific article