{"id":"https://openalex.org/W3168803905","doi":"https://doi.org/10.1137/19m1292011","title":"Partial Regularity of Suitable Weak Solutions of the Navier--Stokes--Planck--Nernst--Poisson Equation","display_name":"Partial Regularity of Suitable Weak Solutions of the Navier--Stokes--Planck--Nernst--Poisson Equation","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3168803905","doi":"https://doi.org/10.1137/19m1292011","mag":"3168803905"},"language":"en","primary_location":{"id":"doi:10.1137/19m1292011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1292011","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","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/A5062662909","display_name":"Huajun Gong","orcid":"https://orcid.org/0000-0002-1924-7789"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Huajun Gong","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080150651","display_name":"Changyou Wang","orcid":"https://orcid.org/0000-0002-8797-0506"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Changyou Wang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100710629","display_name":"Xiaotao Zhang","orcid":"https://orcid.org/0009-0002-3607-6528"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaotao Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062662909"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9703,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.85685629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"53","issue":"3","first_page":"3306","last_page":"3337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9976000189781189,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9902999997138977,"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/mathematics","display_name":"Mathematics","score":0.8319031000137329},{"id":"https://openalex.org/keywords/nernst-equation","display_name":"Nernst equation","score":0.8039216995239258},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.667823076248169},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.5810444951057434},{"id":"https://openalex.org/keywords/weak-solution","display_name":"Weak solution","score":0.5805020928382874},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5706797242164612},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5476351380348206},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5291705131530762},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.5282708406448364},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.5174020528793335},{"id":"https://openalex.org/keywords/hausdorff-measure","display_name":"Hausdorff measure","score":0.4669042229652405},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4548344016075134},{"id":"https://openalex.org/keywords/planck","display_name":"Planck","score":0.4383794367313385},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4146895706653595},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3378780484199524},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14748680591583252},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1320684254169464},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06213247776031494}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8319031000137329},{"id":"https://openalex.org/C184501600","wikidata":"https://www.wikidata.org/wiki/Q751124","display_name":"Nernst equation","level":3,"score":0.8039216995239258},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.667823076248169},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.5810444951057434},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.5805020928382874},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5706797242164612},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5476351380348206},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5291705131530762},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.5282708406448364},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.5174020528793335},{"id":"https://openalex.org/C73225184","wikidata":"https://www.wikidata.org/wiki/Q1591095","display_name":"Hausdorff measure","level":3,"score":0.4669042229652405},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4548344016075134},{"id":"https://openalex.org/C166126730","wikidata":"https://www.wikidata.org/wiki/Q725309","display_name":"Planck","level":2,"score":0.4383794367313385},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4146895706653595},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3378780484199524},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14748680591583252},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1320684254169464},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06213247776031494},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C17525397","wikidata":"https://www.wikidata.org/wiki/Q176140","display_name":"Electrode","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1292011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1292011","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3338363611","display_name":null,"funder_award_id":"61872429","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3636494526","display_name":null,"funder_award_id":"11871345","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4480632070","display_name":null,"funder_award_id":"2101224","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4489669356","display_name":null,"funder_award_id":"1764417","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G626238790","display_name":null,"funder_award_id":"11601342","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7430798095","display_name":null,"funder_award_id":"BX20200135","funder_id":"https://openalex.org/F4320335768","funder_display_name":"National Postdoctoral Program for Innovative Talents"},{"id":"https://openalex.org/G8823245075","display_name":null,"funder_award_id":"11901209","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335768","display_name":"National Postdoctoral Program for Innovative Talents","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1568806775","https://openalex.org/W1966495245","https://openalex.org/W1968474984","https://openalex.org/W1969929913","https://openalex.org/W1975414780","https://openalex.org/W1982967056","https://openalex.org/W2015925226","https://openalex.org/W2021073558","https://openalex.org/W2021316932","https://openalex.org/W2021964921","https://openalex.org/W2030400485","https://openalex.org/W2038162551","https://openalex.org/W2046192257","https://openalex.org/W2046936298","https://openalex.org/W2049133293","https://openalex.org/W2055656807","https://openalex.org/W2058953413","https://openalex.org/W2091176842","https://openalex.org/W2136881310","https://openalex.org/W2137485331","https://openalex.org/W2150824042","https://openalex.org/W2151847866","https://openalex.org/W2323980941","https://openalex.org/W2331593594","https://openalex.org/W2520914149","https://openalex.org/W2525885718","https://openalex.org/W2946483082","https://openalex.org/W3102486899","https://openalex.org/W3124715136"],"related_works":["https://openalex.org/W2379390434","https://openalex.org/W2370474301","https://openalex.org/W2140982806","https://openalex.org/W2363813782","https://openalex.org/W2397516911","https://openalex.org/W2368976343","https://openalex.org/W2047522694","https://openalex.org/W2402543099","https://openalex.org/W29316750","https://openalex.org/W4289143703"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"inspired":[3],"by":[4,8],"the":[5,22,28,36],"seminal":[6],"work":[7],"Caffarelli,":[9],"Kohn,":[10],"and":[11],"Nirenberg":[12],"[Comm.":[13],"Pure":[14],"Appl.":[15],"Math.,":[16],"35":[17],"(1982),":[18],"pp.":[19],"771--831]":[20],"on":[21],"incompressible":[23],"Navier--Stokes":[24],"equation,":[25],"we":[26],"establish":[27],"existence":[29],"of":[30],"a":[31,47],"suitable":[32],"weak":[33],"solution":[34],"to":[35],"Navier--Stokes--Planck--Nernst--Poisson":[37],"equation":[38],"in":[39],"dimension":[40],"three,":[41],"which":[42],"is":[43,55],"smooth":[44],"away":[45],"from":[46],"closed":[48],"set":[49],"whose":[50],"1-dimensional":[51],"parabolic":[52],"Hausdorff":[53],"measure":[54],"zero.":[56]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}