{"id":"https://openalex.org/W2803279879","doi":"https://doi.org/10.1137/18m1202335","title":"Rescaled Objective Solutions of Fokker--Planck and Boltzmann equations","display_name":"Rescaled Objective Solutions of Fokker--Planck and Boltzmann equations","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2803279879","doi":"https://doi.org/10.1137/18m1202335","mag":"2803279879"},"language":"en","primary_location":{"id":"doi:10.1137/18m1202335","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1202335","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1805.10337","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Karsten Matthies","orcid":"https://orcid.org/0000-0001-8250-2538"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karsten Matthies","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-8250-2538","affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Florian Theil","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Florian Theil","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3258,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.76697873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"51","issue":"2","first_page":"1321","last_page":"1348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9092000126838684,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9092000126838684,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.029500000178813934,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.010900000110268593,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.7990000247955322},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5597000122070312},{"id":"https://openalex.org/keywords/boltzmann-constant","display_name":"Boltzmann constant","score":0.5404999852180481},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.486299991607666},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.4268999993801117},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.41760000586509705},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4106000065803528},{"id":"https://openalex.org/keywords/lattice-boltzmann-methods","display_name":"Lattice Boltzmann methods","score":0.373199999332428}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.807699978351593},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.7990000247955322},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6013000011444092},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5597000122070312},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.5404999852180481},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.486299991607666},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.4268999993801117},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.41760000586509705},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4106000065803528},{"id":"https://openalex.org/C21821499","wikidata":"https://www.wikidata.org/wiki/Q1807064","display_name":"Lattice Boltzmann methods","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.35359999537467957},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3506999909877777},{"id":"https://openalex.org/C164916747","wikidata":"https://www.wikidata.org/wiki/Q4382753","display_name":"Direct simulation Monte Carlo","level":4,"score":0.33489999175071716},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C2988492214","wikidata":"https://www.wikidata.org/wiki/Q911951","display_name":"Stationary solution","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2892000079154968},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2754000127315521},{"id":"https://openalex.org/C33932047","wikidata":"https://www.wikidata.org/wiki/Q375553","display_name":"Boltzmann's entropy formula","level":3,"score":0.2750000059604645},{"id":"https://openalex.org/C20892832","wikidata":"https://www.wikidata.org/wiki/Q3271879","display_name":"Circular symmetry","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.26660001277923584},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/18m1202335","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1202335","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"},{"id":"pmh:oai:arXiv.org:1805.10337","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1805.10337","pdf_url":"https://arxiv.org/pdf/1805.10337","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:purehost.bath.ac.uk:openaire/a6c922be-7ad5-441d-9663-d2ab474dbd5c","is_oa":true,"landing_page_url":"https://researchportal.bath.ac.uk/en/publications/a6c922be-7ad5-441d-9663-d2ab474dbd5c","pdf_url":"https://purehost.bath.ac.uk/ws/files/175708772/1805.10337v1.pdf","source":{"id":"https://openalex.org/S4377196294","display_name":"Pure (University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Matthies, K & Theil, F 2019, 'Rescaled Objective Solutions of Fokker-Planck and Boltzmann equations', SIAM Journal on Mathematical Analysis (SIMA), vol. 51, no. 2, pp. 1321\u20131348. https://doi.org/10.1137/18M1202335","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1805.10337","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1805.10337","pdf_url":"https://arxiv.org/pdf/1805.10337","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1611580691","https://openalex.org/W1977657887","https://openalex.org/W1995295970","https://openalex.org/W2006930831","https://openalex.org/W2012205310","https://openalex.org/W2013895420","https://openalex.org/W2027564485","https://openalex.org/W2041246127","https://openalex.org/W2056518217","https://openalex.org/W2064389898","https://openalex.org/W2077070574","https://openalex.org/W2078798756","https://openalex.org/W2081976234","https://openalex.org/W2086251603","https://openalex.org/W2088519718","https://openalex.org/W2101575317","https://openalex.org/W2119536545","https://openalex.org/W2126076178","https://openalex.org/W2130401121","https://openalex.org/W2139649897","https://openalex.org/W2141612068","https://openalex.org/W2160199745","https://openalex.org/W2761199264","https://openalex.org/W2964261763"],"related_works":[],"abstract_inverted_index":{"We":[0,53],"study":[1],"the":[2,9,21,24,30,40,51,56,71,85,89],"long-time":[3,86],"behavior":[4],"of":[5,8,23,32,65],"symmetric":[6],"solutions":[7,25,34,79],"nonlinear":[10,17],"Boltzmann":[11,58],"equation":[12,59,74],"and":[13],"a":[14,82],"closely":[15],"related":[16],"Fokker--Planck":[18,73],"equation.":[19],"If":[20],"symmetry":[22],"corresponds":[26],"to":[27,81],"shear":[28],"flows,":[29],"existence":[31],"stationary":[33,63],"can":[35],"be":[36],"ruled":[37],"out":[38],"because":[39],"energy":[41],"is":[42,92],"not":[43,61,95],"conserved.":[44],"After":[45],"anisotropic":[46],"rescaling,":[47],"both":[48],"equations":[49],"conserve":[50],"energy.":[52],"show":[54],"that":[55,77],"rescaled":[57,72],"does":[60],"admit":[62],"densities":[64],"Maxwellian":[66,83],"type":[67],"(exponentially":[68],"decaying).":[69],"For":[70],"we":[75],"demonstrate":[76],"all":[78],"converge":[80],"in":[84],"limit,":[87],"however,":[88],"convergence":[90],"rate":[91],"only":[93],"algebraic,":[94],"exponential.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2018-06-01T00:00:00"}