Discretely self-similar solutions for 3D MHD equations and global weak solutions in weighted \(L^2\) spaces
type: Item
instance of: scholarly article
title: Discretely self-similar solutions for 3D MHD equations and global weak solutions in weighted \(L^2\) spaces
zbMATH Open document ID: 1461.35181
author: Pedro Gabriel Fernández-Dalgo
author: Oscar Jarrín
published in: Journal of Mathematical Fluid Mechanics
publication date: 2021-02-18T00:00:00Z
review text: 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.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35C06
zbMATH DE Number: 7312805
zbMATH Keywords: magnetohydrodynamics
zbMATH Keywords: weak solutions in weighted spaces
zbMATH Keywords: discretely self-similar solution
zbMATH Keywords: local energy control
MaRDI profile type: Publication
full work available at URL: s00021-020-00551-1
OpenAlex ID: W3122337983
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DOI: 10.1007/S00021-020-00551-1
description: scientific article; zbMATH DE number 7312805