{"id":"https://openalex.org/W2037064345","doi":"https://doi.org/10.1137/13090482x","title":"Pointwise Behavior of the Linearized Boltzmann Equation on a Torus","display_name":"Pointwise Behavior of the Linearized Boltzmann Equation on a Torus","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2037064345","doi":"https://doi.org/10.1137/13090482x","mag":"2037064345"},"language":"en","primary_location":{"id":"doi:10.1137/13090482x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13090482x","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/A5103025613","display_name":"Kung-Chien Wu","orcid":"https://orcid.org/0000-0001-8538-7037"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Kung-Chien Wu","raw_affiliation_strings":["Department of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103025613"],"corresponding_institution_ids":["https://openalex.org/I530967"],"apc_list":null,"apc_paid":null,"fwci":3.0272,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.90234544,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"46","issue":"1","first_page":"639","last_page":"656"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":1.0,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9995999932289124,"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/pointwise","display_name":"Pointwise","score":0.9010388851165771},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8354275226593018},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.7492712140083313},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.6371610760688782},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5804040431976318},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5458614230155945},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.5015699863433838},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.45714643597602844},{"id":"https://openalex.org/keywords/boltzmann-constant","display_name":"Boltzmann constant","score":0.45693153142929077},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.44941386580467224},{"id":"https://openalex.org/keywords/exponential-decay","display_name":"Exponential decay","score":0.44511377811431885},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4271726906299591},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.41337263584136963},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18168678879737854},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.16012874245643616},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10823091864585876},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10539445281028748}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.9010388851165771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8354275226593018},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.7492712140083313},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.6371610760688782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5804040431976318},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5458614230155945},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5015699863433838},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.45714643597602844},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.45693153142929077},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.44941386580467224},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.44511377811431885},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4271726906299591},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.41337263584136963},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18168678879737854},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.16012874245643616},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10823091864585876},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10539445281028748},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/13090482x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13090482x","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:CiteSeerX.psu:10.1.1.766.4403","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.766.4403","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1301.0734.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W969629701","https://openalex.org/W1537383557","https://openalex.org/W1984896804","https://openalex.org/W1987539346","https://openalex.org/W1994725903","https://openalex.org/W2019579692","https://openalex.org/W2039481916","https://openalex.org/W2043934169","https://openalex.org/W2047423653","https://openalex.org/W2048939523","https://openalex.org/W2131014366","https://openalex.org/W2154955497","https://openalex.org/W2963374085","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4309639072","https://openalex.org/W2774769607","https://openalex.org/W2076303422","https://openalex.org/W4388257265","https://openalex.org/W849161923","https://openalex.org/W1579959893","https://openalex.org/W3404850","https://openalex.org/W4388401275","https://openalex.org/W4238782814","https://openalex.org/W4386916460"],"abstract_inverted_index":{"We":[0,67],"study":[1],"the":[2,6,21,37,41,44,48,52,57,62,65,74,83,101,115,119],"pointwise":[3],"behavior":[4],"of":[5,26,36,43,56,64,110,118],"linearized":[7],"Boltzmann":[8],"equation":[9],"on":[10,61],"a":[11,69,107],"torus":[12],"for":[13,47,72],"nonsmooth":[14],"initial":[15],"perturbations.":[16],"The":[17,29,92],"result":[18],"reveals":[19],"both":[20],"fluid":[22],"and":[23,51,86,104,126,135,151],"kinetic":[24],"aspects":[25],"this":[27,111],"model.":[28],"fluid-like":[30,58],"waves":[31,59],"are":[32,80],"constructed":[33],"as":[34],"part":[35],"long-wave":[38],"expansion":[39],"in":[40,99],"spectrum":[42],"Fourier":[45],"modes":[46],"space":[49],"variable,":[50],"time":[53,89],"decay":[54,90],"rate":[55],"depends":[60],"size":[63],"domain.":[66],"design":[68],"Picard-type":[70],"iteration":[71],"constructing":[73,100],"increasingly":[75],"regular":[76],"kinetic-like":[77,102],"waves,":[78,103],"which":[79],"carried":[81],"by":[82],"transport":[84,121],"equations":[85,122],"have":[87],"exponential":[88],"rate.":[91],"mixture":[93],"lemma":[94,112],"plays":[95],"an":[96],"important":[97],"role":[98],"we":[105],"supply":[106],"new":[108],"proof":[109,128],"without":[113],"using":[114],"explicit":[116],"solution":[117],"damped":[120],"(compare":[123],"with":[124],"Liu":[125,150],"Yu's":[127],"[H.":[129],"W.":[130],"Kuo,":[131],"T.":[132],"P.":[133],"Liu,":[134],"S.":[136],"E.":[137],"Noh,":[138],"Bull.":[139],"Inst.":[140],"Math.":[141],"Acad.":[142],"Sin.":[143],"(N.S.),":[144],"5":[145],"(2010),":[146],"pp.":[147,160],"1--10;":[148],"T.-P.":[149],"S.-H.":[152],"Yu,":[153],"Comm.":[154],"Pure":[155],"Appl.":[156],"Math.,":[157],"57":[158],"(2004),":[159],"1543--1608]).":[161]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
