{"id":"https://openalex.org/W2962746182","doi":"https://doi.org/10.1137/140986359","title":"Finite Time Singularities for Hyperbolic Systems","display_name":"Finite Time Singularities for Hyperbolic Systems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2962746182","doi":"https://doi.org/10.1137/140986359","mag":"2962746182"},"language":"en","primary_location":{"id":"doi:10.1137/140986359","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140986359","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/A5100452891","display_name":"Geng Chen","orcid":"https://orcid.org/0000-0002-3452-9434"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Geng Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006807386","display_name":"Tao Huang","orcid":"https://orcid.org/0000-0002-0165-9785"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tao Huang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100373889","display_name":"Chun Liu","orcid":"https://orcid.org/0000-0002-0480-0107"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chun Liu","raw_affiliation_strings":["Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9996,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.75927637,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"47","issue":"1","first_page":"758","last_page":"785"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998999834060669,"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/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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9923999905586243,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.788363516330719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7360861301422119},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.6654164791107178},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.642911434173584},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6175180077552795},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.5506017208099365},{"id":"https://openalex.org/keywords/uniform-boundedness","display_name":"Uniform boundedness","score":0.48962241411209106},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4845244288444519},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.457397997379303},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.42166274785995483},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.41137734055519104}],"concepts":[{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.788363516330719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7360861301422119},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.6654164791107178},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.642911434173584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6175180077552795},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.5506017208099365},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.48962241411209106},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4845244288444519},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.457397997379303},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.42166274785995483},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.41137734055519104},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140986359","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140986359","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1490657362","https://openalex.org/W1550066393","https://openalex.org/W1600967930","https://openalex.org/W1815834322","https://openalex.org/W1986668190","https://openalex.org/W1986854500","https://openalex.org/W1987246040","https://openalex.org/W1987926212","https://openalex.org/W1990084743","https://openalex.org/W1990466218","https://openalex.org/W2011406208","https://openalex.org/W2011669849","https://openalex.org/W2021552186","https://openalex.org/W2044228622","https://openalex.org/W2047996264","https://openalex.org/W2048596004","https://openalex.org/W2053544741","https://openalex.org/W2056778013","https://openalex.org/W2066363083","https://openalex.org/W2076038171","https://openalex.org/W2080049628","https://openalex.org/W2090034374","https://openalex.org/W2094777373","https://openalex.org/W2095014084","https://openalex.org/W2110858186","https://openalex.org/W2121169925","https://openalex.org/W2135630419","https://openalex.org/W2321134557","https://openalex.org/W2481459718","https://openalex.org/W2963855108","https://openalex.org/W2964059519","https://openalex.org/W4238534344"],"related_works":["https://openalex.org/W4319792534","https://openalex.org/W1978812981","https://openalex.org/W4287555507","https://openalex.org/W4206841519","https://openalex.org/W3112767584","https://openalex.org/W3172166105","https://openalex.org/W3103128892","https://openalex.org/W1679891066","https://openalex.org/W2559572050","https://openalex.org/W2962746182"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,12,29,58,80,84,89,94,97,100],"formation":[6],"of":[7,14,60,82,99],"finite":[8,63],"time":[9],"singularities":[10],"in":[11,35,62],"form":[13],"super":[15],"norm":[16],"blowup":[17],"for":[18,65],"a":[19,53],"spatially":[20],"inhomogeneous":[21],"hyperbolic":[22],"system.":[23],"The":[24,50],"system":[25,51],"is":[26],"related":[27],"to":[28],"variational":[30],"wave":[31],"equations":[32],"as":[33],"those":[34],"R.":[36],"Glassey,":[37],"J.":[38],"Hunter,":[39],"and":[40,74,96],"Y.":[41],"Zheng":[42],"[J.":[43],"Differential":[44],"Equations,":[45],"129":[46],"(1996),":[47],"pp.":[48],"49--78].":[49],"possesses":[52],"unique":[54],"$C^1$":[55],"solution":[56],"before":[57],"emergence":[59],"vacuum":[61],"time,":[64],"given":[66],"initial":[67],"data":[68],"that":[69],"are":[70,102],"smooth":[71],"enough,":[72],"bounded,":[73],"uniformly":[75],"away":[76],"from":[77],"vacuum.":[78],"At":[79],"occurrence":[81],"blowup,":[83],"density":[85,98],"becomes":[86],"zero,":[87],"while":[88],"momentum":[90],"stays":[91],"finite;":[92],"however,":[93],"velocity":[95],"energy":[101],"both":[103],"infinity.":[104]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}