{"id":"https://openalex.org/W2941361946","doi":"https://doi.org/10.1002/cpa.21920","title":"Global Mild Solutions of the Landau and Non\u2010Cutoff Boltzmann Equations","display_name":"Global Mild Solutions of the Landau and Non\u2010Cutoff Boltzmann Equations","publication_year":2020,"publication_date":"2020-06-12","ids":{"openalex":"https://openalex.org/W2941361946","doi":"https://doi.org/10.1002/cpa.21920","mag":"2941361946"},"language":"en","primary_location":{"id":"doi:10.1002/cpa.21920","doi":"https://doi.org/10.1002/cpa.21920","is_oa":false,"landing_page_url":"https://doi.org/10.1002/cpa.21920","pdf_url":null,"source":{"id":"https://openalex.org/S134818455","display_name":"Communications on Pure and Applied Mathematics","issn_l":"0010-3640","issn":["0010-3640","1097-0312"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications on Pure and Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1904.12086","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034920062","display_name":"Renjun Duan","orcid":"https://orcid.org/0000-0001-8821-8829","observed_orcids":["https://orcid.org/0000-0001-8821-8829"]},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Renjun Duan","raw_affiliation_strings":["Department of Mathematics The Chinese University of Hong Kong  Shatin Hong Kong P.R. CHINA","Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, P.R. CHINA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics The Chinese University of Hong Kong  Shatin Hong Kong P.R. CHINA","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, P.R. CHINA","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059859467","display_name":"Shuangqian Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I159948400","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62","country_code":"CN","type":"education","lineage":["https://openalex.org/I159948400"]},{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuangqian Liu","raw_affiliation_strings":["Department of Mathematics Jinan Unviersity  Guangzhou 510632 P.R. CHINA","School of Mathematics and Statistics Central China Normal University  Wuhan 430079 P.R. CHINA","Department of Mathematics, Jinan Unviersity, Guangzhou, 510632 P.R. CHINA","School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079 P.R. CHINA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Jinan Unviersity  Guangzhou 510632 P.R. CHINA","institution_ids":["https://openalex.org/I159948400"]},{"raw_affiliation_string":"School of Mathematics and Statistics Central China Normal University  Wuhan 430079 P.R. CHINA","institution_ids":["https://openalex.org/I40963666"]},{"raw_affiliation_string":"Department of Mathematics, Jinan Unviersity, Guangzhou, 510632 P.R. CHINA","institution_ids":["https://openalex.org/I159948400"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079 P.R. CHINA","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067858037","display_name":"Shota Sakamoto","orcid":"https://orcid.org/0000-0002-8509-0484","observed_orcids":["https://orcid.org/0000-0002-8509-0484"]},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shota Sakamoto","raw_affiliation_strings":["Mathematical Institute Tohoku University  Sendai 980\u20100856 JAPAN","Mathematical Institute, Tohoku University, Sendai, 980-0856 JAPAN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute Tohoku University  Sendai 980\u20100856 JAPAN","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Mathematical Institute, Tohoku University, Sendai, 980-0856 JAPAN","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050081333","display_name":"Robert M. Strain","orcid":"https://orcid.org/0000-0002-1107-8570","observed_orcids":["https://orcid.org/0000-0002-1107-8570"]},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert M. Strain","raw_affiliation_strings":["Department of Mathematics University of Pennsylvania, David Rittenhouse Lab  209 South 33rd Street Philadelphia PA 19104\u20106395 USA","Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia, PA, 19104-6395 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Pennsylvania, David Rittenhouse Lab  209 South 33rd Street Philadelphia PA 19104\u20106395 USA","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia, PA, 19104-6395 USA","institution_ids":["https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5034920062"],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":{"value":4000,"currency":"USD","value_usd":4000},"apc_paid":null,"fwci":10.7953,"has_fulltext":true,"cited_by_count":79,"citation_normalized_percentile":{"value":0.99095697,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"74","issue":"5","first_page":"932","last_page":"1020"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9980000257492065,"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":0.9980000257492065,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.0007999999797903001,"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":0.00019999999494757503,"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/landau-equation","display_name":"Landau equation","score":0.972000002861023},{"id":"https://openalex.org/keywords/non-cutoff-boltzmann-equation","display_name":"non-cutoff Boltzmann equation","score":0.9350000023841858},{"id":"https://openalex.org/keywords/global-mild-solutions","display_name":"global mild solutions","score":0.8009999990463257},{"id":"https://openalex.org/keywords/small-amplitude-solutions","display_name":"small amplitude solutions","score":0.9559999704360962},{"id":"https://openalex.org/keywords/coulomb-potential","display_name":"Coulomb potential","score":0.6959999799728394},{"id":"https://openalex.org/keywords/wiener-algebra","display_name":"Wiener algebra","score":0.7300000190734863},{"id":"https://openalex.org/keywords/inlet-boundary-conditions","display_name":"inlet boundary conditions","score":0.9020000100135803},{"id":"https://openalex.org/keywords/specular-reflection-boundary-condition","display_name":"specular reflection boundary condition","score":0.9509999752044678},{"id":"https://openalex.org/keywords/torus","display_name":"torus","score":0.5910000205039978},{"id":"https://openalex.org/keywords/propagation-of-regularity","display_name":"propagation of regularity","score":0.8090000152587891},{"id":"https://openalex.org/keywords/long-time-behavior","display_name":"long-time behavior","score":0.9160000085830688},{"id":"https://openalex.org/keywords/collision-operator","display_name":"collision operator","score":0.4869999885559082}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7842392921447754},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6420707106590271},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.6403999924659729},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5789108872413635},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5651503801345825},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5383255481719971},{"id":"https://openalex.org/C2778217198","wikidata":"https://www.wikidata.org/wiki/Q556977","display_name":"Cutoff","level":2,"score":0.4837951362133026},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4203653335571289},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17004352807998657},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1472190022468567},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1002/cpa.21920","doi":"https://doi.org/10.1002/cpa.21920","is_oa":false,"landing_page_url":"https://doi.org/10.1002/cpa.21920","pdf_url":null,"source":{"id":"https://openalex.org/S134818455","display_name":"Communications on Pure and Applied Mathematics","issn_l":"0010-3640","issn":["0010-3640","1097-0312"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications on Pure and Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1904.12086","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.12086","pdf_url":"https://arxiv.org/pdf/1904.12086","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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:irdb.nii.ac.jp:01211:0006217729","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/2324/7174347","pdf_url":"https://catalog.lib.kyushu-u.ac.jp/opac_download_md/7174347/7174347.pdf","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Communications on Pure and Applied Mathematics","raw_type":"journal article"},{"id":"pmh:oai:catalog.lib.kyushu-u.ac.jp:2324/7174347","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2324/7174347","pdf_url":null,"source":{"id":"https://openalex.org/S4306400832","display_name":"Kyushu University Institutional Repository (QIR) (Kyushu University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I135598925","host_organization_name":"Kyushu University","host_organization_lineage":["https://openalex.org/I135598925"],"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":"1020","raw_type":"journal article"},{"id":"doi:10.48550/arxiv.1904.12086","doi":"https://doi.org/10.48550/arxiv.1904.12086","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1904.12086","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1904.12086","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.12086","pdf_url":"https://arxiv.org/pdf/1904.12086","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3284061071","display_name":"Topics in Fluid dynamics with free boundaries, and Kinetic theory","funder_award_id":"1500916","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3683298662","display_name":"\u52a8\u7406\u5b66\u65b9\u7a0b\u7684\u521d\u8fb9\u503c\u95ee\u9898\u7814\u7a76","funder_award_id":"11971201","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8984790225","display_name":"Analysis of Non-Linear Partial Differential Equations in Free Boundary Fluid Dynamics and Kinetic Theory","funder_award_id":"1764177","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":99,"referenced_works":["https://openalex.org/W28106125","https://openalex.org/W148325819","https://openalex.org/W165153693","https://openalex.org/W230142061","https://openalex.org/W1507939396","https://openalex.org/W1645527346","https://openalex.org/W1649261177","https://openalex.org/W1780201395","https://openalex.org/W1898928021","https://openalex.org/W1913957549","https://openalex.org/W1925947257","https://openalex.org/W1966756553","https://openalex.org/W1966956543","https://openalex.org/W1969092599","https://openalex.org/W1970018499","https://openalex.org/W1975096251","https://openalex.org/W1978390651","https://openalex.org/W1981352579","https://openalex.org/W1985892273","https://openalex.org/W1985898993","https://openalex.org/W1986562502","https://openalex.org/W1989205527","https://openalex.org/W1991491657","https://openalex.org/W1991902795","https://openalex.org/W1998283523","https://openalex.org/W2007196946","https://openalex.org/W2019579692","https://openalex.org/W2023023275","https://openalex.org/W2036881335","https://openalex.org/W2038519360","https://openalex.org/W2039481916","https://openalex.org/W2040663681","https://openalex.org/W2040945051","https://openalex.org/W2045379334","https://openalex.org/W2055066459","https://openalex.org/W2055099692","https://openalex.org/W2056518217","https://openalex.org/W2063541189","https://openalex.org/W2065357833","https://openalex.org/W2082654967","https://openalex.org/W2093321557","https://openalex.org/W2094528868","https://openalex.org/W2095069656","https://openalex.org/W2119655313","https://openalex.org/W2148744212","https://openalex.org/W2150550863","https://openalex.org/W2167967599","https://openalex.org/W2194220232","https://openalex.org/W2222540311","https://openalex.org/W2231608175","https://openalex.org/W2297183116","https://openalex.org/W2310593802","https://openalex.org/W2329895630","https://openalex.org/W2331417883","https://openalex.org/W2337370313","https://openalex.org/W2338765302","https://openalex.org/W2462078800","https://openalex.org/W2498247430","https://openalex.org/W2513014888","https://openalex.org/W2535105190","https://openalex.org/W2559410015","https://openalex.org/W2621284833","https://openalex.org/W2743544228","https://openalex.org/W2760861994","https://openalex.org/W2762647011","https://openalex.org/W2763646373","https://openalex.org/W2764042021","https://openalex.org/W2766537724","https://openalex.org/W2784570379","https://openalex.org/W2799085567","https://openalex.org/W2800328247","https://openalex.org/W2805140136","https://openalex.org/W2807244659","https://openalex.org/W2905345949","https://openalex.org/W2963101821","https://openalex.org/W2963158010","https://openalex.org/W2963278106","https://openalex.org/W2963374085","https://openalex.org/W2963758492","https://openalex.org/W2963822970","https://openalex.org/W2963914308","https://openalex.org/W2972720256","https://openalex.org/W2982765947","https://openalex.org/W3005465185","https://openalex.org/W3098358263","https://openalex.org/W3099067492","https://openalex.org/W3099153579","https://openalex.org/W3101052620","https://openalex.org/W3101423708","https://openalex.org/W3101845240","https://openalex.org/W3103301222","https://openalex.org/W3103499727","https://openalex.org/W3104041939","https://openalex.org/W3104469468","https://openalex.org/W3104892411","https://openalex.org/W3105755904","https://openalex.org/W3105827688","https://openalex.org/W3165098735","https://openalex.org/W4241362023"],"related_works":["https://openalex.org/W3092388660","https://openalex.org/W1778838665","https://openalex.org/W3175879137","https://openalex.org/W2328322229","https://openalex.org/W3094919452","https://openalex.org/W2119262383","https://openalex.org/W4320056724","https://openalex.org/W2090463984","https://openalex.org/W3081363737","https://openalex.org/W2049628683"],"abstract_inverted_index":{"This":[0],"paper":[1],"proves":[2],"the":[3,13,17,21,28,36,51,73,77,89,92,96,101,111,119,124,137,142,147,161,165,170,181,186,193,198,203,207,219,234,243],"existence":[4],"of":[5,38,114,180,192,209,222,236,238,240],"small\u2010amplitude":[6],"global\u2010in\u2010time":[7],"unique":[8],"mild":[9],"solutions":[10,40,63,117,211,223,241],"to":[11,60,68,118,140],"both":[12,225],"Landau":[14,105],"equation":[15,23,75],"including":[16],"Coulomb":[18],"potential":[19,112],"and":[20,32,95,104,190,227,230],"Boltzmann":[22,74,103],"without":[24],"angular":[25],"cutoff.":[26],"Since":[27],"well\u2010known":[29],"works":[30],"[45]":[31],"[3,":[33],"43]":[34],"on":[35],"construction":[37,208],"classical":[39],"in":[41,46,50,64,70,80,100,136,144,188,197,202,212,242],"smooth":[42],"Sobolev":[43],"spaces":[44],"which":[45],"particular":[47],"are":[48],"regular":[49],"spatial":[52,138,148,204,244],"variables,":[53],"it":[54],"still":[55],"remains":[56],"an":[57,65],"open":[58],"problem":[59,143],"obtain":[61],"global":[62,210],"framework,":[66],"similar":[67],"that":[69,185],"[49],":[71],"for":[72,116,224],"with":[76,133,158],"cutoff":[78],"assumption":[79],"general":[81],"bounded":[82],"domains.":[83],"One":[84],"main":[85],"difficulty":[86,109],"arises":[87],"from":[88],"interaction":[90],"between":[91],"transport":[93],"operator":[94,99],"velocity\u2010diffusion\u2010type":[97],"collision":[98],"non\u2010cutoff":[102],"equations;":[106],"another":[107],"major":[108],"is":[110,150,175,184,196],"formation":[113],"singularities":[115],"boundary":[120,167,173],"value":[121],"problem.":[122],"In":[123],"present":[125],"work":[126],"we":[127,216,231],"introduce":[128],"a":[129,152,155],"new":[130],"function":[131,182,195,214],"space":[132,183],"low":[134],"regularity":[135,239],"variable":[139],"treat":[141],"cases":[145],"when":[146],"domain":[149],"either":[151,164],"torus":[153],"or":[154,169],"finite":[156],"channel":[157],"boundary.":[159],"For":[160],"latter":[162],"case,":[163],"inflow":[166],"condition":[168,174],"specular":[171],"reflection":[172],"considered.":[176],"An":[177],"important":[178],"property":[179,235],"norm,":[187],"velocity":[189],"time,":[191],"distribution":[194],"Wiener":[199],"algebra":[200],"A(\u03a9)":[201],"variables.":[205,245],"Besides":[206],"these":[213],"spaces,":[215],"additionally":[217],"study":[218],"large\u2010time":[220],"behavior":[221],"hard":[226],"soft":[228],"potentials,":[229],"further":[232],"justify":[233],"propagation":[237],"\u00a9":[246],"2019":[247],"Wiley":[248],"Periodicals,":[249],"Inc.":[250]},"counts_by_year":[{"year":2026,"cited_by_count":11},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2019-05-03T00:00:00"}
