{"id":"https://openalex.org/W7115196910","doi":"https://doi.org/10.1109/tac.2025.3644127","title":"Exponential Stability of the Linearized Viscous Saint-Venant Equations Using a Quadratic Lyapunov Function","display_name":"Exponential Stability of the Linearized Viscous Saint-Venant Equations Using a Quadratic Lyapunov Function","publication_year":2025,"publication_date":"2025-12-15","ids":{"openalex":"https://openalex.org/W7115196910","doi":"https://doi.org/10.1109/tac.2025.3644127"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3644127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3644127","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2603.06411","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Amaury Hayat","orcid":"https://orcid.org/0000-0002-7017-1097"},"institutions":[{"id":"https://openalex.org/I142631665","display_name":"\u00c9cole nationale des ponts et chauss\u00e9es","ror":"https://ror.org/02nwvxz07","country_code":"FR","type":"education","lineage":["https://openalex.org/I142631665","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Amaury Hayat","raw_affiliation_strings":["Ecole Nationale des Ponts et Chauss&#x00E9;es, Institut Polytechnique de Paris, Champs-sur-Marne, France"],"raw_orcid":"https://orcid.org/0000-0002-7017-1097","affiliations":[{"raw_affiliation_string":"Ecole Nationale des Ponts et Chauss&#x00E9;es, Institut Polytechnique de Paris, Champs-sur-Marne, France","institution_ids":["https://openalex.org/I142631665"]}]},{"author_position":"last","author":{"id":null,"display_name":"Nathan Lichtl\u00e9","orcid":"https://orcid.org/0000-0002-5521-6517"},"institutions":[{"id":"https://openalex.org/I142631665","display_name":"\u00c9cole nationale des ponts et chauss\u00e9es","ror":"https://ror.org/02nwvxz07","country_code":"FR","type":"education","lineage":["https://openalex.org/I142631665","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nathan Lichtl\u00e9","raw_affiliation_strings":["Ecole Nationale des Ponts et Chauss&#x00E9;es, Institut Polytechnique de Paris, Champs-sur-Marne, France"],"raw_orcid":"https://orcid.org/0000-0002-5521-6517","affiliations":[{"raw_affiliation_string":"Ecole Nationale des Ponts et Chauss&#x00E9;es, Institut Polytechnique de Paris, Champs-sur-Marne, France","institution_ids":["https://openalex.org/I142631665"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I142631665"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.51581604,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"6","first_page":"3575","last_page":"3587"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.6762999892234802,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.6762999892234802,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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":0.1469999998807907,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.02500000037252903,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/lyapunov-function","display_name":"Lyapunov function","score":0.7343000173568726},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5712000131607056},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5503000020980835},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5349000096321106},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.46050000190734863},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4244999885559082},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.4212999939918518},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.40450000762939453}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7343000173568726},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7278000116348267},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5938000082969666},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5712000131607056},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5503000020980835},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5349000096321106},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.46050000190734863},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4244999885559082},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.4212999939918518},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.40450000762939453},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40380001068115234},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3824999928474426},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3743000030517578},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.3709000051021576},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.311599999666214},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.26840001344680786},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.257999986410141}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tac.2025.3644127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3644127","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2603.06411","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2603.06411","pdf_url":"https://arxiv.org/pdf/2603.06411","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05540717v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05540717","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://ieeexplore.ieee.org/document/11299581","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2603.06411","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2603.06411","pdf_url":"https://arxiv.org/pdf/2603.06411","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3199539279","display_name":"Stabilization of nonlinear partial differential equations: theory and methods","funder_award_id":"ANR-24-ERCS-0010","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3],"investigate":[4],"the":[5,9,16,26,31,53,101,104,120,124,128,132],"exponential":[6,121],"stability":[7,122],"of":[8,30,39,55,103,123],"viscous":[10],"Saint-Venant":[11,19,32],"equations":[12,20,33,43],"by":[13],"adding":[14],"to":[15],"standard":[17],"hyperbolic":[18],"a":[21,112],"viscosity":[22,40,92],"term":[23],"coming":[24],"from":[25,34],"higher":[27],"order":[28],"approximation":[29],"Navier-Stokes":[35],"equations.":[36],"The":[37],"inclusion":[38],"transforms":[41],"these":[42],"into":[44],"more":[45],"complex":[46],"second-order":[47],"partial":[48],"differential":[49],"equations,":[50],"accurately":[51],"modeling":[52],"behavior":[54],"real-world":[56],"fluids":[57],"that":[58,71,80,108],"inherently":[59],"possess":[60],"viscosity.":[61],"We":[62,95],"construct":[63],"an":[64],"explicit":[65,97],"quadratic":[66,82,113],"Lyapunov":[67,83,114],"function":[68,115],"and":[69],"demonstrate":[70],"it":[72],"must":[73],"be":[74],"diagonal":[75],"in":[76,86,131],"physical":[77],"coordinates,":[78],"revealing":[79],"certain":[81],"functions":[84],"effective":[85],"non-viscous":[87],"cases":[88],"become":[89],"inadequate":[90],"when":[91],"is":[93],"introduced.":[94],"find":[96],"sufficient":[98],"conditions":[99,106],"on":[100],"parameters":[102],"boundary":[105],"such":[107],"for":[109],"small":[110],"viscosities":[111],"exists.":[116],"This":[117],"result":[118],"ensures":[119],"linearized":[125],"system":[126],"around":[127],"steady-state":[129],"solutions":[130],"<inline-formula":[133],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[134],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[135],"notation=\"LaTeX\">$L^{2}$</tex-math></inline-formula>":[136],"norm.":[137]},"counts_by_year":[],"updated_date":"2026-05-30T06:14:24.967023","created_date":"2025-12-15T00:00:00"}
