{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T07:34:30Z","timestamp":1767771270169,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T00:00:00Z","timestamp":1617840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"I.N.D.A.M-G.N.A.M.P.A. 2019 and RUDN University","award":["I.N.D.A.M-G.N.A.M.P.A. 2019 and RUDN University"],"award-info":[{"award-number":["I.N.D.A.M-G.N.A.M.P.A. 2019 and RUDN University"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we investigate the regularity of weak solutions to the 3D incompressible MHD equations. We provide a regularity criterion for weak solutions involving any two groups functions (\u22021u1,\u22021b1), (\u22022u2,\u22022b2) and (\u22023u3,\u22023b3) in anisotropic Lorentz space.<\/jats:p>","DOI":"10.3390\/sym13040625","type":"journal-article","created":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T21:27:44Z","timestamp":1617917264000},"page":"625","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz Spaces"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6611-6370","authenticated-orcid":false,"given":"Maria Alessandra","family":"Ragusa","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Catania, Viale Andrea Doria No. 6, 95128 Catania, Italy"},{"name":"RUDN University, Miklukho-Maklay St, 117198 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fan","family":"Wu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/BF00250512","article-title":"In\u00e9quations en thermo\u00e9lasticit\u00e9 et magn\u00e9tohydrodynamique","volume":"46","author":"Duvaut","year":"1972","journal-title":"Arch. 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