{"id":"https://openalex.org/W3145373051","doi":"https://doi.org/10.3390/sym13040625","title":"Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz Spaces","display_name":"Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz Spaces","publication_year":2021,"publication_date":"2021-04-08","ids":{"openalex":"https://openalex.org/W3145373051","doi":"https://doi.org/10.3390/sym13040625","mag":"3145373051"},"language":"en","primary_location":{"id":"doi:10.3390/sym13040625","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040625","pdf_url":"https://www.mdpi.com/2073-8994/13/4/625/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/4/625/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060302514","display_name":"Maria Alessandra Ragusa","orcid":"https://orcid.org/0000-0001-6611-6370"},"institutions":[{"id":"https://openalex.org/I126527374","display_name":"Peoples' Friendship University of Russia","ror":"https://ror.org/02dn9h927","country_code":"RU","type":"education","lineage":["https://openalex.org/I126527374"]},{"id":"https://openalex.org/I39063666","display_name":"University of Catania","ror":"https://ror.org/03a64bh57","country_code":"IT","type":"education","lineage":["https://openalex.org/I39063666"]}],"countries":["IT","RU"],"is_corresponding":true,"raw_author_name":"Maria Alessandra Ragusa","raw_affiliation_strings":["Department of Mathematics, University of Catania, Viale Andrea Doria No. 6, 95128 Catania, Italy","RUDN University, Miklukho-Maklay St, 117198 Moscow, Russia"],"raw_orcid":"https://orcid.org/0000-0001-6611-6370","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Catania, Viale Andrea Doria No. 6, 95128 Catania, Italy","institution_ids":["https://openalex.org/I39063666"]},{"raw_affiliation_string":"RUDN University, Miklukho-Maklay St, 117198 Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003136525","display_name":"Fan Wu","orcid":"https://orcid.org/0000-0003-2367-4916"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fan Wu","raw_affiliation_strings":["Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China","institution_ids":["https://openalex.org/I173759888"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5060302514"],"corresponding_institution_ids":["https://openalex.org/I126527374","https://openalex.org/I39063666"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.6509,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.8199458,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"13","issue":"4","first_page":"625","last_page":"625"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9695000052452087,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lorentz-transformation","display_name":"Lorentz transformation","score":0.8044489622116089},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.7576541304588318},{"id":"https://openalex.org/keywords/magnetohydrodynamics","display_name":"Magnetohydrodynamics","score":0.6957368850708008},{"id":"https://openalex.org/keywords/lorentz-space","display_name":"Lorentz space","score":0.665463387966156},{"id":"https://openalex.org/keywords/lorentz-force","display_name":"Lorentz force","score":0.5924460291862488},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5695723295211792},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5375492572784424},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.488619863986969},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48324570059776306},{"id":"https://openalex.org/keywords/magneto","display_name":"Magneto","score":0.43845927715301514},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43548649549484253},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.4229600727558136},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.23269835114479065},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1994040608406067},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16331976652145386},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07112583518028259}],"concepts":[{"id":"https://openalex.org/C5667645","wikidata":"https://www.wikidata.org/wiki/Q217255","display_name":"Lorentz transformation","level":2,"score":0.8044489622116089},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.7576541304588318},{"id":"https://openalex.org/C31532427","wikidata":"https://www.wikidata.org/wiki/Q2549249","display_name":"Magnetohydrodynamics","level":3,"score":0.6957368850708008},{"id":"https://openalex.org/C2776551381","wikidata":"https://www.wikidata.org/wiki/Q6680542","display_name":"Lorentz space","level":3,"score":0.665463387966156},{"id":"https://openalex.org/C140190676","wikidata":"https://www.wikidata.org/wiki/Q172137","display_name":"Lorentz force","level":3,"score":0.5924460291862488},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5695723295211792},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5375492572784424},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.488619863986969},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48324570059776306},{"id":"https://openalex.org/C171636128","wikidata":"https://www.wikidata.org/wiki/Q1307177","display_name":"Magneto","level":3,"score":0.43845927715301514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43548649549484253},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4229600727558136},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.23269835114479065},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1994040608406067},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16331976652145386},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07112583518028259},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13040625","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040625","pdf_url":"https://www.mdpi.com/2073-8994/13/4/625/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:78620d5db12544eba513402ecc0fb2d7","is_oa":true,"landing_page_url":"https://doaj.org/article/78620d5db12544eba513402ecc0fb2d7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 4, p 625 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/4/625/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13040625","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13040625","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040625","pdf_url":"https://www.mdpi.com/2073-8994/13/4/625/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6898653562","display_name":null,"funder_award_id":"5-100","funder_id":"https://openalex.org/F4320329913","funder_display_name":"RUDN University"}],"funders":[{"id":"https://openalex.org/F4320329913","display_name":"RUDN University","ror":"https://ror.org/02dn9h927"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3145373051.pdf","grobid_xml":"https://content.openalex.org/works/W3145373051.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W944174965","https://openalex.org/W1491966250","https://openalex.org/W1550467807","https://openalex.org/W1968010296","https://openalex.org/W1985817879","https://openalex.org/W1991281189","https://openalex.org/W1996243255","https://openalex.org/W2003364345","https://openalex.org/W2006547990","https://openalex.org/W2033933633","https://openalex.org/W2039749880","https://openalex.org/W2053593122","https://openalex.org/W2058484969","https://openalex.org/W2117686126","https://openalex.org/W2149568842","https://openalex.org/W2151210652","https://openalex.org/W2151847866","https://openalex.org/W2312282965","https://openalex.org/W2337975624","https://openalex.org/W2467577930","https://openalex.org/W2518423756","https://openalex.org/W2762803637","https://openalex.org/W2771099311","https://openalex.org/W2807971296","https://openalex.org/W2898454889","https://openalex.org/W2903097267","https://openalex.org/W2963960791","https://openalex.org/W2964300614","https://openalex.org/W2971067876","https://openalex.org/W2973166085","https://openalex.org/W3040988303","https://openalex.org/W3100869599","https://openalex.org/W3118824425","https://openalex.org/W3129926033","https://openalex.org/W6703788170"],"related_works":["https://openalex.org/W4381708517","https://openalex.org/W2060791159","https://openalex.org/W1974677088","https://openalex.org/W1596721677","https://openalex.org/W2950359495","https://openalex.org/W2803200311","https://openalex.org/W2508164662","https://openalex.org/W2113733528","https://openalex.org/W1985230058","https://openalex.org/W2381444803"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"investigate":[4],"the":[5,11],"regularity":[6,19],"of":[7],"weak":[8,22],"solutions":[9,23],"to":[10],"3D":[12],"incompressible":[13],"MHD":[14],"equations.":[15],"We":[16],"provide":[17],"a":[18],"criterion":[20],"for":[21],"involving":[24],"any":[25],"two":[26],"groups":[27],"functions":[28],"(\u22021u1,\u22021b1),":[29],"(\u22022u2,\u22022b2)":[30],"and":[31],"(\u22023u3,\u22023b3)":[32],"in":[33],"anisotropic":[34],"Lorentz":[35],"space.":[36]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4}],"updated_date":"2026-05-23T08:51:43.019350","created_date":"2025-10-10T00:00:00"}
