{"id":"https://openalex.org/W4385617726","doi":"https://doi.org/10.1515/cmam-2023-0052","title":"Space-Time Approximation of Local Strong Solutions to the 3D Stochastic Navier\u2013Stokes Equations","display_name":"Space-Time Approximation of Local Strong Solutions to the 3D Stochastic Navier\u2013Stokes Equations","publication_year":2023,"publication_date":"2023-08-07","ids":{"openalex":"https://openalex.org/W4385617726","doi":"https://doi.org/10.1515/cmam-2023-0052"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2023-0052","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2023-0052","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018745301","display_name":"Dominic Breit","orcid":"https://orcid.org/0000-0003-2787-3250"},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]},{"id":"https://openalex.org/I43980791","display_name":"Clausthal University of Technology","ror":"https://ror.org/04qb8nc58","country_code":"DE","type":"education","lineage":["https://openalex.org/I43980791"]}],"countries":["DE","GB"],"is_corresponding":true,"raw_author_name":"Dominic Breit","raw_affiliation_strings":["Institute of Mathematics , TU Clausthal , Erzstra\u00dfe 1, 38678 Clausthal-Zellerfeld , Germany ; and Department of Mathematics, Heriot-Watt University, Riccarton Edinburgh EH14 4AS, United Kingdom"],"raw_orcid":"https://orcid.org/0000-0003-2787-3250","affiliations":[{"raw_affiliation_string":"Institute of Mathematics , TU Clausthal , Erzstra\u00dfe 1, 38678 Clausthal-Zellerfeld , Germany ; and Department of Mathematics, Heriot-Watt University, Riccarton Edinburgh EH14 4AS, United Kingdom","institution_ids":["https://openalex.org/I43980791","https://openalex.org/I32062511"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041571733","display_name":"Alan Dodgson","orcid":null},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alan Dodgson","raw_affiliation_strings":["Department of Mathematics , Heriot-Watt University , Riccarton Edinburgh EH14 4AS , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Heriot-Watt University , Riccarton Edinburgh EH14 4AS , United Kingdom","institution_ids":["https://openalex.org/I32062511"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018745301"],"corresponding_institution_ids":["https://openalex.org/I32062511","https://openalex.org/I43980791"],"apc_list":null,"apc_paid":null,"fwci":1.1077,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.78701261,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"24","issue":"3","first_page":"577","last_page":"597"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8463423252105713},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7367551326751709},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7050321102142334},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.6973875761032104},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5252988934516907},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4911489188671112},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4849010109901428},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.4720856845378876},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4673502743244171},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45232897996902466},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.4389961063861847},{"id":"https://openalex.org/keywords/discrete-time-stochastic-process","display_name":"Discrete-time stochastic process","score":0.412801057100296},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.21742463111877441},{"id":"https://openalex.org/keywords/continuous-time-stochastic-process","display_name":"Continuous-time stochastic process","score":0.18075963854789734},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1411432921886444},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10800805687904358},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0887778103351593}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8463423252105713},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7367551326751709},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7050321102142334},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.6973875761032104},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5252988934516907},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4911489188671112},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4849010109901428},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.4720856845378876},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4673502743244171},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45232897996902466},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.4389961063861847},{"id":"https://openalex.org/C92703954","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Discrete-time stochastic process","level":4,"score":0.412801057100296},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.21742463111877441},{"id":"https://openalex.org/C158535547","wikidata":"https://www.wikidata.org/wiki/Q5165437","display_name":"Continuous-time stochastic process","level":3,"score":0.18075963854789734},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1411432921886444},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10800805687904358},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0887778103351593},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C76178495","wikidata":"https://www.wikidata.org/wiki/Q4808784","display_name":"Asset (computer security)","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":1,"locations":[{"id":"doi:10.1515/cmam-2023-0052","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2023-0052","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.7799999713897705}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W6548635","https://openalex.org/W1581851824","https://openalex.org/W1983679522","https://openalex.org/W1993988025","https://openalex.org/W1994731994","https://openalex.org/W2015535719","https://openalex.org/W2051708601","https://openalex.org/W2051912300","https://openalex.org/W2066145581","https://openalex.org/W2133020871","https://openalex.org/W2323964977","https://openalex.org/W2478294287","https://openalex.org/W2612485807","https://openalex.org/W2620284697","https://openalex.org/W2784215314","https://openalex.org/W2964063216","https://openalex.org/W2979313970","https://openalex.org/W3132552728","https://openalex.org/W3134694139","https://openalex.org/W3203845654","https://openalex.org/W4220819434","https://openalex.org/W4226484436","https://openalex.org/W4252104256","https://openalex.org/W4300475775","https://openalex.org/W4380301712","https://openalex.org/W4387954836"],"related_works":["https://openalex.org/W2912324827","https://openalex.org/W2789985026","https://openalex.org/W2171105877","https://openalex.org/W2095435264","https://openalex.org/W3123169305","https://openalex.org/W2022292713","https://openalex.org/W1603461487","https://openalex.org/W2913519323","https://openalex.org/W2098954817","https://openalex.org/W2477147293"],"abstract_inverted_index":{"Abstract":[0],"We":[1,26],"consider":[2],"the":[3,9,15,32,64,68,80],"3D":[4],"stochastic":[5],"Navier\u2013Stokes":[6],"equation":[7],"on":[8,75],"torus.":[10],"Our":[11,71],"main":[12],"result":[13,60],"concerns":[14],"temporal":[16],"and":[17,51],"spatio-temporal":[18],"discretisation":[19],"of":[20,44,52,67],"a":[21],"local":[22],"strong":[23],"pathwise":[24],"solution.":[25,70,82],"prove":[27],"optimal":[28],"convergence":[29,38,43],"rates":[30],"for":[31,79],"energy":[33],"error":[34],"with":[35],"respect":[36],"to":[37,63],"in":[39,49,57],"probability,":[40],"that":[41],"is":[42,73],"order":[45,53],"(up":[46,54],"to)":[47,55],"1":[48],"space":[50],"1/2":[56],"time.":[58],"The":[59],"holds":[61],"up":[62],"possible":[65],"blow-up":[66],"(time-discrete)":[69,81],"approach":[72],"based":[74],"discrete":[76],"stopping":[77],"times":[78]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}