{"id":"https://openalex.org/W3106640576","doi":"https://doi.org/10.1137/20m1315439","title":"Persistence of the Steady Normal Shock Structure for the Unsteady Potential Flow","display_name":"Persistence of the Steady Normal Shock Structure for the Unsteady Potential Flow","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3106640576","doi":"https://doi.org/10.1137/20m1315439","mag":"3106640576"},"language":"en","primary_location":{"id":"doi:10.1137/20m1315439","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1315439","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":true,"oa_status":"green","oa_url":"https://scholars.cityu.edu.hk/en/publications/persistence-of-the-steady-normal-shock-structure-for-the-unsteady","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014050871","display_name":"Beixiang Fang","orcid":"https://orcid.org/0000-0002-7226-9266"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Beixiang Fang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009803148","display_name":"Wei Xiang","orcid":"https://orcid.org/0000-0002-8937-9322"},"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":false,"raw_author_name":"Wei Xiang","raw_affiliation_strings":["Department of Mathematics"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064156596","display_name":"Feng Xiao","orcid":"https://orcid.org/0000-0002-9843-3570"},"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":false,"raw_author_name":"Feng Xiao","raw_affiliation_strings":["Department of Mathematics"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014050871"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1807,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.77069124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"52","issue":"6","first_page":"6033","last_page":"6104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9988999962806702,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.7918508052825928},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6269734501838684},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6098793148994446},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5454226136207581},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5423643589019775},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.49942874908447266},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4729066789150238},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.44925081729888916},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"Free boundary problem","score":0.4410209655761719},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3470582962036133},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09071195125579834},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07169973850250244}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7918508052825928},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6269734501838684},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6098793148994446},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5454226136207581},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5423643589019775},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.49942874908447266},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4729066789150238},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.44925081729888916},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.4410209655761719},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3470582962036133},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09071195125579834},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07169973850250244},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/20m1315439","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1315439","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"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/persistence-of-the-steady-normal-shock-structure-for-the-unsteady","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fang, B, Xiang, W & Xiao, F 2020, 'PERSISTENCE OF THE STEADY NORMAL SHOCK STRUCTURE FOR THE UNSTEADY POTENTIAL FLOW', SIAM Journal on Mathematical Analysis, vol. 52, no. 6, pp. 6033-6104. https://doi.org/10.1137/20M1315439","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/57cc2fc7-173b-4388-8f91-768ac41a77c5","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/57cc2fc7-173b-4388-8f91-768ac41a77c5","pdf_url":"https://scholars.cityu.edu.hk/files/188642407/70281224.pdf","source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Fang, B, Xiang, W & Xiao, F 2020, 'PERSISTENCE OF THE STEADY NORMAL SHOCK STRUCTURE FOR THE UNSTEADY POTENTIAL FLOW', SIAM Journal on Mathematical Analysis, vol. 52, no. 6, pp. 6033-6104. https://doi.org/10.1137/20M1315439","raw_type":"article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/persistence-of-the-steady-normal-shock-structure-for-the-unsteady","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fang, B, Xiang, W & Xiao, F 2020, 'PERSISTENCE OF THE STEADY NORMAL SHOCK STRUCTURE FOR THE UNSTEADY POTENTIAL FLOW', SIAM Journal on Mathematical Analysis, vol. 52, no. 6, pp. 6033-6104. https://doi.org/10.1137/20M1315439","raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.47999998927116394,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3010357957","display_name":null,"funder_award_id":"CityU 11303518","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4877445586","display_name":null,"funder_award_id":"D1502","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5542335259","display_name":null,"funder_award_id":"11971308","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6148491908","display_name":null,"funder_award_id":"11304817","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G6221780053","display_name":null,"funder_award_id":"11971","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6693727020","display_name":null,"funder_award_id":"CityU 11304820","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G6933977322","display_name":null,"funder_award_id":"CityU 11304817","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G7033253288","display_name":null,"funder_award_id":"Grants","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7479256935","display_name":null,"funder_award_id":"11332916","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G7584932508","display_name":null,"funder_award_id":"15XD1502300","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7889403753","display_name":null,"funder_award_id":"11303518","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G8162905225","display_name":null,"funder_award_id":"1197130","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8536467974","display_name":null,"funder_award_id":"11371250","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8615497951","display_name":null,"funder_award_id":"15XD1502300","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G8691113572","display_name":null,"funder_award_id":"11631008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"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":43,"referenced_works":["https://openalex.org/W1538526245","https://openalex.org/W1963870305","https://openalex.org/W1964757934","https://openalex.org/W1994517289","https://openalex.org/W2003270736","https://openalex.org/W2008876382","https://openalex.org/W2019152430","https://openalex.org/W2027337196","https://openalex.org/W2028097513","https://openalex.org/W2029920217","https://openalex.org/W2035422267","https://openalex.org/W2037312561","https://openalex.org/W2059060905","https://openalex.org/W2061544666","https://openalex.org/W2062154247","https://openalex.org/W2065383968","https://openalex.org/W2068611762","https://openalex.org/W2077827601","https://openalex.org/W2086395947","https://openalex.org/W2092345883","https://openalex.org/W2094365289","https://openalex.org/W2094432683","https://openalex.org/W2094888429","https://openalex.org/W2106961716","https://openalex.org/W2117182957","https://openalex.org/W2121846460","https://openalex.org/W2143419031","https://openalex.org/W2150323068","https://openalex.org/W2166644351","https://openalex.org/W2166730672","https://openalex.org/W2203500596","https://openalex.org/W2502127214","https://openalex.org/W2771031773","https://openalex.org/W2780086666","https://openalex.org/W2787657780","https://openalex.org/W2900551824","https://openalex.org/W2962715636","https://openalex.org/W2963520672","https://openalex.org/W2963678070","https://openalex.org/W2963749583","https://openalex.org/W3012021409","https://openalex.org/W3035614913","https://openalex.org/W3128809158"],"related_works":["https://openalex.org/W2754834382","https://openalex.org/W4301492515","https://openalex.org/W2563901864","https://openalex.org/W1984112382","https://openalex.org/W2953252165","https://openalex.org/W1586418441","https://openalex.org/W2066412970","https://openalex.org/W3168009835","https://openalex.org/W4299072667","https://openalex.org/W2393913967"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,27,56,62,136,207,276],"devoted":[3],"to":[4,93,149,154,163,178,212,218,247,260],"the":[5,8,11,30,57,68,72,82,89,94,99,112,139,151,169,179,182,185,189,196,200,203,210,213,230,240,248,261,266,269],"study":[6],"of":[7,10,33,39,117,121,141,171,181,188,199,263,268],"stability":[9,25],"steady":[12],"normal":[13],"shock":[14],"structure":[15],"in":[16,44,98,124,202,229,256,265],"potential":[17],"flows":[18],"under":[19],"an":[20,34,108],"unsteady":[21],"perturbation.":[22],"The":[23,53,133,237],"dynamic":[24],"problem":[26,32,38,70,116,153,250],"formulated":[28],"as":[29,97],"well-posedness":[31],"initial":[35,113],"boundary":[36,114],"value":[37,115],"a":[40,45,50,125,142,155,164,272],"nonlinear":[41,214],"wave":[42],"equation":[43],"cornered":[46,90,126,231],"space":[47,91,127,232],"domain":[48,92,128,166,233],"with":[49,220,255],"free":[51],"boundary.":[52],"corner":[54],"singularity":[55],"essential":[58],"difficulty":[59],"and":[60,225],"there":[61],"no":[63],"result":[64,110],"available":[65],"even":[66,161],"for":[67,111,209],"linear":[69,118,152,242],"without":[71,129],"symmetry":[73,131,183],"assumptions,":[74,184],"i.e.,":[75],"\u201ceven\u201d":[76],"or":[77],"\u201codd\u201d":[78],"traces":[79],"vanish":[80],"on":[81,138,239],"solid":[83],"boundary,":[84],"which":[85,146,206],"allows":[86,147],"extension":[87],"from":[88,194],"half-space":[95,165],"domain,":[96,205],"previous":[100],"works.":[101],"In":[102,216],"this":[103,257],"paper,":[104],"we":[105,252],"first":[106],"obtain":[107],"existence":[109,170],"hyperbolic":[119,223],"equations":[120],"second":[122],"order":[123,217],"such":[130,167],"assumptions.":[132],"key":[134],"idea":[135],"based":[137],"construction":[140],"new":[143,156,222],"auxilliary":[144],"problem,":[145,271],"us":[148,193],"reduce":[150],"one":[157],"that":[158,168,251],"can":[159,173,244],"be":[160,174,245],"extended":[162,190,204],"$H_\\eta^2$-solutions":[172],"established.":[175],"However,":[176],"due":[177],"lack":[180],"low":[186],"regularity":[187,198,264],"coefficients":[191],"block":[192],"obtaining":[195],"higher":[197],"solutions":[201],"necessary":[208],"iteration":[211,275],"problem.":[215],"deal":[219],"it,":[221],"type":[224,227],"elliptic":[226],"estimates":[228,267],"are":[234,253],"established":[235],"carefully.":[236],"results":[238],"general":[241],"problems":[243],"applied":[246],"linearized":[249,270],"concerned":[254],"paper.":[258],"Due":[259],"loss":[262],"modified":[273],"Nash--Moser":[274],"developed.":[277]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-04T08:04:53.788161","created_date":"2025-10-10T00:00:00"}
