{"id":"https://openalex.org/W7213276166","doi":"https://doi.org/10.48550/arxiv.2609.15095","title":"Optimal Time-Decay of global solutions to the Navier-Stokes-Maxwell system","display_name":"Optimal Time-Decay of global solutions to the Navier-Stokes-Maxwell system","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213276166","doi":"https://doi.org/10.48550/arxiv.2609.15095"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.15095","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15095","pdf_url":"https://arxiv.org/pdf/2609.15095","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.15095","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058573357","display_name":"Haroune Houamed","orcid":"https://orcid.org/0000-0002-0385-9000","observed_orcids":["https://orcid.org/0000-0002-0385-9000"]},"institutions":[{"id":"https://openalex.org/I1351752","display_name":"Ko\u00e7 University","ror":"https://ror.org/00jzwgz36","country_code":"TR","type":"education","lineage":["https://openalex.org/I1351752"]},{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA","TR"],"is_corresponding":false,"raw_author_name":"Houamed, Haroune","raw_affiliation_strings":["Koc \u00b8University , Istanbul , Turkey","University of Victoria , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Koc \u00b8University , Istanbul , Turkey","institution_ids":["https://openalex.org/I1351752"]},{"raw_affiliation_string":"University of Victoria , Canada","institution_ids":["https://openalex.org/I212119943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151825747","display_name":"Slim Ibrahim","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1351752","display_name":"Ko\u00e7 University","ror":"https://ror.org/00jzwgz36","country_code":"TR","type":"education","lineage":["https://openalex.org/I1351752"]},{"id":"https://openalex.org/I29891158","display_name":"University of Sharjah","ror":"https://ror.org/00engpz63","country_code":"AE","type":"education","lineage":["https://openalex.org/I29891158"]}],"countries":["AE","TR"],"is_corresponding":false,"raw_author_name":"Ibrahim, Slim","raw_affiliation_strings":["Koc \u00b8University , Istanbul , Turkey","University of Sharjah , United Arab Emirates"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Koc \u00b8University , Istanbul , Turkey","institution_ids":["https://openalex.org/I1351752"]},{"raw_affiliation_string":"University of Sharjah , United Arab Emirates","institution_ids":["https://openalex.org/I29891158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001203951","display_name":"Belkacem Said\u2010Houari","orcid":"https://orcid.org/0000-0003-4876-2293","observed_orcids":["https://orcid.org/0000-0003-4876-2293"]},"institutions":[{"id":"https://openalex.org/I1351752","display_name":"Ko\u00e7 University","ror":"https://ror.org/00jzwgz36","country_code":"TR","type":"education","lineage":["https://openalex.org/I1351752"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Said-Houari, Belkacem","raw_affiliation_strings":["Koc \u00b8University , Istanbul , Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Koc \u00b8University , Istanbul , Turkey","institution_ids":["https://openalex.org/I1351752"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9994999766349792,"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":0.9994999766349792,"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":0.0003000000142492354,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.0,"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/global-existence-and-uniqueness","display_name":"global existence and uniqueness","score":0.8009999990463257},{"id":"https://openalex.org/keywords/small-initial-data","display_name":"small initial data","score":0.9259999990463257},{"id":"https://openalex.org/keywords/besov-spaces","display_name":"Besov spaces","score":0.8450000286102295},{"id":"https://openalex.org/keywords/optimal-decay-rates","display_name":"optimal decay rates","score":0.7789999842643738},{"id":"https://openalex.org/keywords/lyapunov-functional","display_name":"Lyapunov functional","score":0.9580000042915344},{"id":"https://openalex.org/keywords/fourier-splitting-method","display_name":"Fourier splitting method","score":0.9670000076293945},{"id":"https://openalex.org/keywords/long-time-behavior","display_name":"long-time behavior","score":0.7590000033378601},{"id":"https://openalex.org/keywords/nonrelativistic-limit","display_name":"non-relativistic limit","score":0.9039999842643738},{"id":"https://openalex.org/keywords/magnetohydrodynamics","display_name":"magnetohydrodynamics","score":0.8980000019073486},{"id":"https://openalex.org/keywords/critical-spaces","display_name":"critical spaces","score":0.32100000977516174}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8230000138282776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7139999866485596},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6948000192642212},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5906999707221985},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5550000071525574},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4952000081539154},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4740000069141388},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4399000108242035},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.43790000677108765},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.42160001397132874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4036000072956085},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.3986999988555908},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.38350000977516174},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.362199991941452},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.2971999943256378},{"id":"https://openalex.org/C65092005","wikidata":"https://www.wikidata.org/wiki/Q7885107","display_name":"Uniform limit theorem","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C2779280203","wikidata":"https://www.wikidata.org/wiki/Q17121211","display_name":"Small data","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C42471609","wikidata":"https://www.wikidata.org/wiki/Q1779048","display_name":"Magnetohydrodynamic drive","level":4,"score":0.2754000127315521},{"id":"https://openalex.org/C2776551381","wikidata":"https://www.wikidata.org/wiki/Q6680542","display_name":"Lorentz space","level":3,"score":0.27489998936653137},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2554999887943268}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.15095","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15095","pdf_url":"https://arxiv.org/pdf/2609.15095","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.15095","doi":"https://doi.org/10.48550/arxiv.2609.15095","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.15095","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.15095","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15095","pdf_url":"https://arxiv.org/pdf/2609.15095","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213276166.pdf","grobid_xml":"https://content.openalex.org/works/W7213276166.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4406549449"],"related_works":["https://openalex.org/W7214774962","https://openalex.org/W4213370523","https://openalex.org/W2769068257","https://openalex.org/W2962969567","https://openalex.org/W2526356816","https://openalex.org/W2922000776","https://openalex.org/W4390242374","https://openalex.org/W4408012977","https://openalex.org/W4289305337","https://openalex.org/W2398517259"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,10,19,32,36,41,50,58,79,83,94,105,112,117,120,135,143,152,156],"existence":[3,114],"and":[4,86],"uniqueness":[5],"of":[6,57,93,119,137],"global-in-time":[7],"solutions":[8],"to":[9,40,78,98,116,134,150],"Navier--Stokes--Maxwell":[11],"(NSM)":[12],"system":[13],"for":[14,64,155],"small":[15],"initial":[16,37],"data":[17,38],"in":[18,26,60,142],"critical":[20],"Fujita--Kato":[21],"space":[22,43],"$\\dot":[23,44,61],"H^{\\frac{d}{2}-1}(\\mathbb":[24],"R^d)$,":[25,46,63],"any":[27,65],"dimension":[28],"$d\\geq":[29],"3$.":[30],"Under":[31],"additional":[33],"assumption":[34],"that":[35,75,129],"belong":[39],"Besov":[42],"B^{-\\frac{d}{2}}_{2,\\infty}(\\mathbb":[45],"we":[47],"also":[48],"establish":[49,99],"optimal":[51,101],"decay":[52,102],"rate":[53],"$t^{-\\frac{s}{2}-\\frac{d}{4}}$":[54],"at":[55],"infinity":[56],"solution":[59],"H^s(\\mathbb":[62],"$s\\in\\left(-\\frac{d}{2},\\frac{d}{2}-1\\right]$.":[66],"This":[67],"is":[68,76,124,130],"achieved":[69],"by":[70,87],"constructing":[71],"a":[72,127],"Lyapunov":[73],"functional":[74],"equivalent":[77],"pointwise":[80],"energy":[81],"on":[82],"Fourier":[84,95],"side,":[85],"combining":[88],"it":[89],"with":[90,132],"an":[91],"adaptation":[92],"splitting":[96],"method":[97],"its":[100],"rate.":[103],"All":[104],"analysis":[106],"carried":[107],"out":[108],"here":[109],"-":[110,123],"from":[111],"global":[113],"theory":[115],"study":[118],"large-time":[121],"behavior":[122],"performed":[125],"within":[126],"framework":[128],"uniform":[131],"respect":[133],"speed":[136],"light":[138],"$c\\in(0,\\infty)$.":[139],"In":[140],"particular,":[141],"non-relativistic":[144],"limit":[145],"$c\\to\\infty$,":[146],"this":[147],"allows":[148],"us":[149],"recover":[151],"same":[153],"results":[154],"corresponding":[157],"limiting":[158],"magnetohydrodynamic":[159],"system.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}
