{"id":"https://openalex.org/W2095129273","doi":"https://doi.org/10.1137/120879919","title":"Vacuum Behaviors around Rarefaction Waves to 1D Compressible Navier--Stokes Equations with Density-Dependent Viscosity","display_name":"Vacuum Behaviors around Rarefaction Waves to 1D Compressible Navier--Stokes Equations with Density-Dependent Viscosity","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2095129273","doi":"https://doi.org/10.1137/120879919","mag":"2095129273"},"language":"en","primary_location":{"id":"doi:10.1137/120879919","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120879919","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/A5016812181","display_name":"Quansen Jiu","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Quansen Jiu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101829732","display_name":"Yi Wang","orcid":"https://orcid.org/0000-0002-5793-8142"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Wang","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences,#TAB#"],"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences,#TAB#","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101898018","display_name":"Zhouping Xin","orcid":"https://orcid.org/0000-0002-7434-2404"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhouping Xin","raw_affiliation_strings":["The Chinese University of Hong Kong"],"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016812181"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.7563,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.97257807,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"45","issue":"5","first_page":"3194","last_page":"3228"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9969000220298767,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9469000101089478,"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/rarefaction","display_name":"Rarefaction (ecology)","score":0.8194077014923096},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6681270599365234},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.6312997341156006},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6291506290435791},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.5106354355812073},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4583124816417694},{"id":"https://openalex.org/keywords/shock-wave","display_name":"Shock wave","score":0.4216836988925934},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3729076683521271},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.32703328132629395},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.19207483530044556}],"concepts":[{"id":"https://openalex.org/C132705693","wikidata":"https://www.wikidata.org/wiki/Q7294543","display_name":"Rarefaction (ecology)","level":3,"score":0.8194077014923096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6681270599365234},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.6312997341156006},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6291506290435791},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5106354355812073},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4583124816417694},{"id":"https://openalex.org/C70477161","wikidata":"https://www.wikidata.org/wiki/Q190688","display_name":"Shock wave","level":2,"score":0.4216836988925934},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3729076683521271},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.32703328132629395},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.19207483530044556},{"id":"https://openalex.org/C62648534","wikidata":"https://www.wikidata.org/wiki/Q706937","display_name":"Species diversity","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120879919","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120879919","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":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8399999737739563}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W59832175","https://openalex.org/W168720733","https://openalex.org/W1665737553","https://openalex.org/W1969543804","https://openalex.org/W1978042660","https://openalex.org/W1979393169","https://openalex.org/W1979870967","https://openalex.org/W1985991323","https://openalex.org/W1987671809","https://openalex.org/W1988758438","https://openalex.org/W1989231059","https://openalex.org/W1992913018","https://openalex.org/W1997482974","https://openalex.org/W2000708166","https://openalex.org/W2013185524","https://openalex.org/W2021111340","https://openalex.org/W2030289593","https://openalex.org/W2030587235","https://openalex.org/W2032309950","https://openalex.org/W2035843479","https://openalex.org/W2051452262","https://openalex.org/W2057711336","https://openalex.org/W2067693029","https://openalex.org/W2070890910","https://openalex.org/W2078187711","https://openalex.org/W2088954885","https://openalex.org/W2094551280","https://openalex.org/W2127065883","https://openalex.org/W2160365034","https://openalex.org/W2168162898","https://openalex.org/W2169827385","https://openalex.org/W2319552480","https://openalex.org/W3139651940","https://openalex.org/W4253117495"],"related_works":["https://openalex.org/W2000908640","https://openalex.org/W2313357499","https://openalex.org/W1969320878","https://openalex.org/W1971848844","https://openalex.org/W2034146741","https://openalex.org/W6247801","https://openalex.org/W2800583016","https://openalex.org/W2393733735","https://openalex.org/W2059546648","https://openalex.org/W2068937774"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,16,38,54,61,65,78,89,96,105,123,133,141,168,182,189,193],"large":[6],"time":[7],"asymptotic":[8],"behavior":[9],"toward":[10],"rarefaction":[11,35,55,106,145,194],"waves":[12,146],"for":[13,24,77,131],"solutions":[14],"to":[15,37,104,109,140],"one-dimensional":[17],"compressible":[18],"Navier--Stokes":[19],"equations":[20,41],"with":[21,42,68,111],"density-dependent":[22],"viscosities":[23],"general":[25,69],"initial":[26,66,124],"data":[27,67],"whose":[28],"far":[29,127],"fields":[30],"are":[31,82],"connected":[32,108],"by":[33,59],"a":[34,49,73],"wave":[36,56,107],"corresponding":[39],"Euler":[40],"one":[43],"end":[44],"state":[45],"being":[46],"vacuum.":[47],"First,":[48],"global-in-time":[50],"weak":[51,93,183],"solution":[52,94,184],"around":[53],"is":[57,86,136,179],"constructed":[58],"approximating":[60],"system":[62],"and":[63,71,80,99,154],"regularizing":[64],"perturbations,":[70],"some":[72],"priori":[74],"uniform-in-time":[75],"estimates":[76,101],"energy":[79,98],"entropy":[81,100],"obtained.":[83],"Then":[84],"it":[85,178],"shown":[87],"that":[88,122,181],"density":[90],"of":[91,143,192],"any":[92],"satisfying":[95],"natural":[97],"will":[102,129,172],"converge":[103],"vacuum":[110,125,170,190],"arbitrary":[112],"strength":[113],"in":[114,120,137,148,174],"sup-norm":[115],"time-asymptotically.":[116],"Our":[117],"results":[118],"imply,":[119],"particular,":[121],"at":[126],"field":[128],"remain":[130],"all":[132,167],"time,":[134],"which":[135],"sharp":[138],"contrast":[139],"case":[142],"nonvacuum":[144],"studied":[147],"[Q.":[149],"S.":[150],"Jiu,":[151],"Y.":[152],"Wang,":[153],"Z.":[155],"P.":[156],"Xin,":[157],"Comm.":[158],"Partial":[159],"Differential":[160],"Equations,":[161],"36":[162],"(2011),":[163],"pp.":[164],"602--634],":[165],"where":[166],"possible":[169],"states":[171],"vanish":[173],"finite":[175],"time.":[176],"Finally,":[177],"proved":[180],"becomes":[185],"regular":[186],"away":[187],"from":[188],"region":[191],"wave.":[195]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}