{"id":"https://openalex.org/W2925340712","doi":"https://doi.org/10.1137/19m1252375","title":"Gaussian Lower Bounds for the Boltzmann Equation without Cutoff","display_name":"Gaussian Lower Bounds for the Boltzmann Equation without Cutoff","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2925340712","doi":"https://doi.org/10.1137/19m1252375","mag":"2925340712"},"language":"en","primary_location":{"id":"doi:10.1137/19m1252375","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1252375","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1903.11278","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048574470","display_name":"Cyril Imbert","orcid":"https://orcid.org/0000-0002-1290-8257"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cyril Imbert","raw_affiliation_strings":["DMA"],"affiliations":[{"raw_affiliation_string":"DMA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060848970","display_name":"Cl\u00e9ment Mouhot","orcid":"https://orcid.org/0000-0002-4755-5404"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cl\u00e9ment Mouhot","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049086637","display_name":"Lu\u00eds Silvestre","orcid":"https://orcid.org/0000-0003-1806-8647"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luis Silvestre","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048574470"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8771,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6788403,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"52","issue":"3","first_page":"2930","last_page":"2944"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9998000264167786,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9950000047683716,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cutoff","display_name":"Cutoff","score":0.8503970503807068},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7023921012878418},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6783171892166138},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6765566468238831},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.645344078540802},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.534529447555542},{"id":"https://openalex.org/keywords/boltzmann-constant","display_name":"Boltzmann constant","score":0.5105689764022827},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4850439429283142},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4209159314632416},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.40055906772613525},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3292933702468872},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3097389340400696},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16183403134346008}],"concepts":[{"id":"https://openalex.org/C2778217198","wikidata":"https://www.wikidata.org/wiki/Q556977","display_name":"Cutoff","level":2,"score":0.8503970503807068},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7023921012878418},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6783171892166138},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6765566468238831},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.645344078540802},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.534529447555542},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.5105689764022827},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4850439429283142},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4209159314632416},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40055906772613525},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3292933702468872},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3097389340400696},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16183403134346008}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/19m1252375","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1252375","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:1903.11278","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.11278","pdf_url":"https://arxiv.org/pdf/1903.11278","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":"","raw_type":"text"},{"id":"mag:2925340712","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1903.11278.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-02078069v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-02078069","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.archives-ouvertes.fr/hal-02078069","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-02078069v2","is_oa":true,"landing_page_url":"https://hal.science/hal-02078069","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://epubs.siam.org/doi/10.1137/19M1252375","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1903.11278","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1903.11278","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1903.11278","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.11278","pdf_url":"https://arxiv.org/pdf/1903.11278","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":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.6800000071525574}],"awards":[{"id":"https://openalex.org/G3340367341","display_name":null,"funder_award_id":"MAFRAN","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G62434199","display_name":null,"funder_award_id":"DMS-1254332","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7705038354","display_name":null,"funder_award_id":"DMS-1362525","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/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W8456792","https://openalex.org/W230142061","https://openalex.org/W1484979569","https://openalex.org/W1966956543","https://openalex.org/W1977732367","https://openalex.org/W2007196946","https://openalex.org/W2023023275","https://openalex.org/W2034393593","https://openalex.org/W2035637414","https://openalex.org/W2036881335","https://openalex.org/W2051589524","https://openalex.org/W2056518217","https://openalex.org/W2128072272","https://openalex.org/W2169704717","https://openalex.org/W2315196406","https://openalex.org/W2321175406","https://openalex.org/W2334374518","https://openalex.org/W2584849287","https://openalex.org/W2785276010","https://openalex.org/W2963278106","https://openalex.org/W2963374085","https://openalex.org/W2963822970","https://openalex.org/W2964023345","https://openalex.org/W2972720256","https://openalex.org/W2982765947","https://openalex.org/W2984129616","https://openalex.org/W2986966993","https://openalex.org/W3002210460","https://openalex.org/W3021960516","https://openalex.org/W3100186321","https://openalex.org/W3100371990"],"related_works":["https://openalex.org/W2128072272","https://openalex.org/W3175476678","https://openalex.org/W2986966993","https://openalex.org/W3100371990","https://openalex.org/W3100186321","https://openalex.org/W3030079222","https://openalex.org/W2763646373","https://openalex.org/W2952047257","https://openalex.org/W1978894893","https://openalex.org/W3197888293","https://openalex.org/W3004085075","https://openalex.org/W2951570470","https://openalex.org/W2760861994","https://openalex.org/W2034805228","https://openalex.org/W2803704036","https://openalex.org/W2337370313","https://openalex.org/W3102512091","https://openalex.org/W1539355408","https://openalex.org/W2953198080","https://openalex.org/W2131848320"],"abstract_inverted_index":{"The":[0,144],"study":[1],"of":[2,4,25,74,116],"positivity":[3],"solutions":[5,106],"to":[6,12,107],"the":[7,22,72,108,114,128,151,160],"Boltzmann":[8,109],"equation":[9,110],"goes":[10],"back":[11],"[T.":[13],"Carleman,":[14],"Acta":[15],"Math.,":[16,184],"60":[17],"(1933),":[18],"pp.":[19,40,50,60,69,172,187,201],"91--146],":[20],"and":[21,32,98,118,126,138,155,178,191],"initial":[23],"argument":[24],"Carleman":[26],"was":[27],"developed":[28],"in":[29,113,164],"[A.":[30],"Pulvirenti":[31],"B.":[33],"Wennberg,":[34],"Comm.":[35,44,167],"Math.":[36,168,196],"Phys.,":[37,169],"183":[38],"(1997),":[39],"145--160;":[41],"C.":[42,174,176,189],"Mouhot,":[43,177],"Partial":[45],"Differential":[46],"Equations,":[47],"30":[48],"(2005),":[49],"881--917;":[51],"M.":[52,62],"Briant,":[53,63],"Arch.":[54],"Ration.":[55],"Mech.":[56],"Anal.,":[57],"218":[58],"(2015),":[59,68],"985--1041;":[61],"Kinet.":[64],"Relat.":[65],"Models,":[66],"8":[67],"281--308]":[70],"but":[71],"appearance":[73],"a":[75,101],"lower":[76,103],"bound":[77,104,154],"with":[78,122],"Gaussian":[79,102],"decay":[80],"had":[81],"remained":[82],"an":[83],"open":[84],"question":[85,97],"for":[86,105],"long-range":[87],"interactions":[88],"(the":[89],"so-called":[90],"noncutoff":[91],"collision":[92],"kernels).":[93],"We":[94],"answer":[95],"this":[96],"establish":[99],"such":[100],"without":[111],"cutoff,":[112],"case":[115],"hard":[117],"moderately":[119],"soft":[120],"potentials,":[121],"spatial":[123],"periodic":[124],"conditions,":[125],"under":[127],"sole":[129],"assumption":[130],"that":[131],"hydrodynamic":[132],"quantities":[133],"(local":[134],"mass,":[135],"local":[136,139],"energy,":[137],"entropy":[140],"density)":[141],"remain":[142],"bounded.":[143],"paper":[145],"is":[146],"mostly":[147],"self-contained,":[148],"apart":[149],"from":[150],"$L^\\infty$":[152],"upper":[153],"weak":[156],"Harnack":[157],"inequality":[158],"on":[159],"solution":[161],"established,":[162],"respectively":[163],"[L.":[165],"Silvestre,":[166,180,193],"348":[170],"(2016),":[171],"69--100;":[173],"Imbert,":[175],"L.":[179,192],"J.":[181,194],"\u00c9c.":[182],"polytech.":[183],"7":[185],"(2020),":[186,200],"143--184.;":[188],"Imbert":[190],"Eur.":[195],"Soc.":[197],"(JEMS),":[198],"22":[199],"507--592].":[202]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
