{"id":"https://openalex.org/W7214799705","doi":"https://doi.org/10.48550/arxiv.2609.35365","title":"Local stability of direct Mach configurations","display_name":"Local stability of direct Mach configurations","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214799705","doi":"https://doi.org/10.48550/arxiv.2609.35365"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.35365","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35365","pdf_url":"https://arxiv.org/pdf/2609.35365","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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.35365","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153428096","display_name":"Jun Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I161350542","display_name":"China Three Gorges University","ror":"https://ror.org/0419nfc77","country_code":"CN","type":"education","lineage":["https://openalex.org/I161350542"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Jun","raw_affiliation_strings":["Three Gorges Mathematical Research Center , China Three Gorges University , No. 8 University Road , Yichang , Hubei 443002 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Three Gorges Mathematical Research Center , China Three Gorges University , No. 8 University Road , Yichang , Hubei 443002 , China","institution_ids":["https://openalex.org/I161350542"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5138466750","display_name":"Xuemei Deng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I161350542","display_name":"China Three Gorges University","ror":"https://ror.org/0419nfc77","country_code":"CN","type":"education","lineage":["https://openalex.org/I161350542"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Deng, Xuemei","raw_affiliation_strings":["Three Gorges Mathematical Research Center , China Three Gorges University , No. 8 University Road , Yichang , Hubei 443002 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Three Gorges Mathematical Research Center , China Three Gorges University , No. 8 University Road , Yichang , Hubei 443002 , China","institution_ids":["https://openalex.org/I161350542"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I161350542"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.5356000065803528,"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"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.5356000065803528,"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"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.42410001158714294,"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":0.011699999682605267,"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/local-stability","display_name":"local stability","score":0.9229999780654907},{"id":"https://openalex.org/keywords/compressible-euler-equations","display_name":"compressible Euler equations","score":0.9120000004768372},{"id":"https://openalex.org/keywords/contact-discontinuity","display_name":"contact discontinuity","score":0.6340000033378601},{"id":"https://openalex.org/keywords/mach-stem","display_name":"Mach stem","score":0.5929999947547913},{"id":"https://openalex.org/keywords/slip-lines","display_name":"slip lines","score":0.7070000171661377},{"id":"https://openalex.org/keywords/reflected-shock-waves","display_name":"reflected shock waves","score":0.8159999847412109},{"id":"https://openalex.org/keywords/incident-shock","display_name":"incident shock","score":0.828000009059906},{"id":"https://openalex.org/keywords/transversality-conditions","display_name":"transversality conditions","score":0.8939999938011169},{"id":"https://openalex.org/keywords/lagrangian-coordinates","display_name":"Lagrangian coordinates","score":0.7730000019073486},{"id":"https://openalex.org/keywords/mixed-boundary-value-problem","display_name":"mixed boundary value problem","score":0.8510000109672546},{"id":"https://openalex.org/keywords/discontinuous-coefficients","display_name":"discontinuous coefficients","score":0.7139999866485596},{"id":"https://openalex.org/keywords/a-priori-estimates","display_name":"a priori estimates","score":0.6159999966621399},{"id":"https://openalex.org/keywords/steady-compressible-flow","display_name":"steady compressible flow","score":0.5709999799728394}],"concepts":[{"id":"https://openalex.org/C165231844","wikidata":"https://www.wikidata.org/wiki/Q160669","display_name":"Mach number","level":2,"score":0.727400004863739},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5424000024795532},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5271999835968018},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4108000099658966},{"id":"https://openalex.org/C169889854","wikidata":"https://www.wikidata.org/wiki/Q6723332","display_name":"Mach reflection","level":4,"score":0.4092000126838684},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.40389999747276306},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.38100001215934753},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.37119999527931213},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36550000309944153},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.3564999997615814},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.35280001163482666},{"id":"https://openalex.org/C5192115","wikidata":"https://www.wikidata.org/wiki/Q2705141","display_name":"Compressible flow","level":3,"score":0.3504999876022339},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.34369999170303345},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3262999951839447},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C107119854","wikidata":"https://www.wikidata.org/wiki/Q775708","display_name":"Mach wave","level":3,"score":0.31029999256134033},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C527307","wikidata":"https://www.wikidata.org/wiki/Q370906","display_name":"Angle of attack","level":3,"score":0.28439998626708984},{"id":"https://openalex.org/C195268267","wikidata":"https://www.wikidata.org/wiki/Q1928883","display_name":"Slip (aerodynamics)","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C13393347","wikidata":"https://www.wikidata.org/wiki/Q8424","display_name":"Aerodynamics","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C70477161","wikidata":"https://www.wikidata.org/wiki/Q190688","display_name":"Shock wave","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C134853933","wikidata":"https://www.wikidata.org/wiki/Q208641","display_name":"Hydrostatic equilibrium","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C122824865","wikidata":"https://www.wikidata.org/wiki/Q830787","display_name":"Hypersonic speed","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C2781300812","wikidata":"https://www.wikidata.org/wiki/Q178061","display_name":"Shock (circulatory)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C2781217745","wikidata":"https://www.wikidata.org/wiki/Q1053779","display_name":"Euler system","level":3,"score":0.25529998540878296},{"id":"https://openalex.org/C102500504","wikidata":"https://www.wikidata.org/wiki/Q6674017","display_name":"Longitudinal static stability","level":3,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.35365","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35365","pdf_url":"https://arxiv.org/pdf/2609.35365","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":"doi:10.48550/arxiv.2609.35365","doi":"https://doi.org/10.48550/arxiv.2609.35365","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.35365","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.35365","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35365","pdf_url":"https://arxiv.org/pdf/2609.35365","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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G8587030525","display_name":null,"funder_award_id":"2025AFB530","funder_id":"https://openalex.org/F4320322186","funder_display_name":"Natural Science Foundation of Hubei Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322186","display_name":"Natural Science Foundation of Hubei Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214799705.pdf","grobid_xml":"https://content.openalex.org/works/W7214799705.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1986082874","https://openalex.org/W2094365289","https://openalex.org/W2037743205","https://openalex.org/W2256132009","https://openalex.org/W2828907590","https://openalex.org/W2277665142","https://openalex.org/W3203589688","https://openalex.org/W1569403960","https://openalex.org/W1990509993","https://openalex.org/W2962715636"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,10,44,51,60,68,83,87,90,93,97,102,113,118,123,144,156,166,170,178,202,213,216],"local":[3],"stability":[4],"of":[5,24,67,82,120,215],"direct":[6],"Mach":[7,20,32,75,94],"configurations":[8],"for":[9,165,195,212],"two-dimensional":[11],"steady":[12],"compressible":[13],"Euler":[14,158],"equations.":[15],"Given":[16],"a":[17,28,31,35,47,56,74,79,124,134,150,161,184,196],"piecewise":[18],"constant":[19],"configuration":[21,76],"that":[22,77,89,130,201],"consists":[23],"an":[25],"incident":[26],"shock,":[27,30,92],"reflected":[29,91],"stem":[33,95],"and":[34,55,96,153,169],"slip":[36,98],"line,":[37,99],"with":[38,101,177,192],"subsonic":[39,104],"downstream":[40,103],"states,":[41],"we":[42],"prove":[43],"following:":[45],"under":[46],"transversality":[48],"condition":[49,58],"on":[50,59],"shock":[52],"polar":[53],"loops":[54],"suitable":[57],"truncation":[61],"segment,":[62],"every":[63],"sufficiently":[64],"small":[65,80,132],"perturbation":[66,81],"incoming":[69,128],"flow":[70,167],"gives":[71],"rise":[72],"to":[73,108,142,154,160,182],"is":[78,115,181],"background":[84,110],"one,":[85],"in":[86,117,133,175,189],"sense":[88],"together":[100],"flow,":[105],"stay":[106],"close":[107],"their":[109],"counterparts;":[111],"moreover,":[112],"solution":[114],"unique":[116],"class":[119],"solutions":[121,214],"satisfying":[122],"priori":[125],"estimate":[126],"(for":[127],"flows":[129],"are":[131,140,206],"slightly":[135],"stronger":[136],"norm).":[137],"Lagrangian":[138],"coordinates":[139],"employed":[141],"transform":[143],"unknown":[145],"contact":[146,179,203],"discontinuity":[147,180,204],"curve":[148],"into":[149],"fixed":[151],"boundary":[152,186],"reduce":[155],"full":[157],"system":[159,164],"first-order":[162],"elliptic":[163,198,217],"direction":[168],"pressure.":[171],"The":[172],"key":[173],"idea":[174],"dealing":[176],"solve":[183],"mixed":[185],"value":[187],"problem,":[188],"divergence":[190],"form":[191],"discontinuous":[193],"coefficients,":[194],"single":[197],"equation,":[199],"so":[200],"conditions":[205,211],"naturally":[207],"preserved":[208],"as":[209],"compatibility":[210],"problem.":[218]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-30T00:00:00"}