{"id":"https://openalex.org/W7214477152","doi":"https://doi.org/10.1080/03605302.2026.2735909","title":"Liouville type theorem and kinetic formulation for 2\u00d72 systems of conservation laws","display_name":"Liouville type theorem and kinetic formulation for 2\u00d72 systems of conservation laws","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214477152","doi":"https://doi.org/10.1080/03605302.2026.2735909"},"language":"en","primary_location":{"id":"doi:10.1080/03605302.2026.2735909","doi":"https://doi.org/10.1080/03605302.2026.2735909","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03605302.2026.2735909","pdf_url":null,"source":{"id":"https://openalex.org/S185232611","display_name":"Communications in Partial Differential Equations","issn_l":"0360-5302","issn":["0360-5302","1532-4133"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Partial Differential Equations","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2502.12840","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040865071","display_name":"Fabio Ancona","orcid":"https://orcid.org/0000-0002-2686-5470","observed_orcids":["https://orcid.org/0000-0002-2686-5470"]},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fabio Ancona","raw_affiliation_strings":["Dipartimento di Matematica \u201cTullio Levi Civita\u201d, Universit\u00e0 di Padova"],"raw_orcid":"https://orcid.org/0000-0002-2686-5470","affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u201cTullio Levi Civita\u201d, Universit\u00e0 di Padova","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027258831","display_name":"Elio Marconi","orcid":"https://orcid.org/0000-0003-2989-2594","observed_orcids":["https://orcid.org/0000-0003-2989-2594"]},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Elio Marconi","raw_affiliation_strings":["Dipartimento di Matematica \u201cTullio Levi Civita\u201d, Universit\u00e0 di Padova"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u201cTullio Levi Civita\u201d, Universit\u00e0 di Padova","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5094346920","display_name":"Luca Talamini","orcid":"https://orcid.org/0009-0008-5147-5184","observed_orcids":["https://orcid.org/0009-0008-5147-5184"]},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Luca Talamini","raw_affiliation_strings":["Mathematics Area, SISSA"],"raw_orcid":"https://orcid.org/0009-0008-5147-5184","affiliations":[{"raw_affiliation_string":"Mathematics Area, SISSA","institution_ids":["https://openalex.org/I138549579"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5094346920"],"corresponding_institution_ids":["https://openalex.org/I138549579"],"apc_list":null,"apc_paid":null,"fwci":8.4088,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.98433299,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"51","issue":"10","first_page":"1139","last_page":"1166"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.5449000000953674,"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":0.5449000000953674,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.06279999762773514,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.05130000039935112,"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/kinetic-formulation","display_name":"kinetic formulation","score":0.8190000057220459},{"id":"https://openalex.org/keywords/entropy-generation","display_name":"entropy production","score":0.8769999742507935},{"id":"https://openalex.org/keywords/liouville-type-theorems","display_name":"Liouville-type theorems","score":0.8949999809265137},{"id":"https://openalex.org/keywords/vanishing-mean-oscillation","display_name":"vanishing mean oscillation","score":0.972000002861023},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.8330000042915344}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8831999897956848},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.7315000295639038},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5903000235557556},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5317000150680542},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.4950999915599823},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.49129998683929443},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44200000166893005},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.413100004196167},{"id":"https://openalex.org/C179434709","wikidata":"https://www.wikidata.org/wiki/Q899853","display_name":"H-theorem","level":5,"score":0.4027999937534332},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.3919999897480011},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38909998536109924},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.3379000127315521},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C2776548862","wikidata":"https://www.wikidata.org/wiki/Q2694495","display_name":"Existence theorem","level":2,"score":0.33090001344680786},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3237999975681305},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.3102000057697296},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.2831999957561493},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.27559998631477356},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.275299996137619},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C206929604","wikidata":"https://www.wikidata.org/wiki/Q530152","display_name":"Picard\u2013Lindel\u00f6f theorem","level":3,"score":0.263700008392334},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.257099986076355},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.2526000142097473}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/03605302.2026.2735909","doi":"https://doi.org/10.1080/03605302.2026.2735909","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03605302.2026.2735909","pdf_url":null,"source":{"id":"https://openalex.org/S185232611","display_name":"Communications in Partial Differential Equations","issn_l":"0360-5302","issn":["0360-5302","1532-4133"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Partial Differential Equations","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2502.12840","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2502.12840","pdf_url":"https://arxiv.org/pdf/2502.12840","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.2502.12840","doi":"https://doi.org/10.48550/arxiv.2502.12840","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2502.12840","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2502.12840","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2502.12840","pdf_url":"https://arxiv.org/pdf/2502.12840","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/G3345895242","display_name":null,"funder_award_id":"H2020-MSCA","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G5245466801","display_name":null,"funder_award_id":"PRIN 2022","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G5796505130","display_name":null,"funder_award_id":"PRIN 2022 PNRR","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214477152.pdf","grobid_xml":"https://content.openalex.org/works/W7214477152.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W47858079","https://openalex.org/W1480714962","https://openalex.org/W1965236651","https://openalex.org/W1982305009","https://openalex.org/W1990492870","https://openalex.org/W1994710706","https://openalex.org/W1994930222","https://openalex.org/W2003277691","https://openalex.org/W2017042872","https://openalex.org/W2018745887","https://openalex.org/W2041664202","https://openalex.org/W2051014922","https://openalex.org/W2073006041","https://openalex.org/W2118653974","https://openalex.org/W2155389855","https://openalex.org/W2322772418","https://openalex.org/W2478358989","https://openalex.org/W2573847088","https://openalex.org/W2747245324","https://openalex.org/W2962985589","https://openalex.org/W2963650358","https://openalex.org/W2972926354","https://openalex.org/W3020161032","https://openalex.org/W3153587463","https://openalex.org/W4238313514","https://openalex.org/W4287644104","https://openalex.org/W4319458790","https://openalex.org/W4387406869","https://openalex.org/W4388105124","https://openalex.org/W4388322678","https://openalex.org/W4400376210","https://openalex.org/W4405510435","https://openalex.org/W4415292257","https://openalex.org/W4415847897","https://openalex.org/W7147462925"],"related_works":["https://openalex.org/W4407759790","https://openalex.org/W7147462925","https://openalex.org/W4415234074","https://openalex.org/W2024998495","https://openalex.org/W1509607831","https://openalex.org/W7165658918","https://openalex.org/W129711303","https://openalex.org/W1990492870","https://openalex.org/W2027648480","https://openalex.org/W7099748997"],"abstract_inverted_index":{"We":[0,11],"study":[1],"L\u221e":[2],"entropy":[3,18,41,69],"solutions":[4,21,38],"to":[5,35],"2\u00d72":[6],"systems":[7],"of":[8,25,58,75,84],"conservation":[9],"laws.":[10],"show":[12],"that,":[13],"if":[14],"a":[15,23,46,82],"uniformly":[16],"convex":[17],"exists,":[19],"these":[20],"satisfy":[22],"pair":[24],"kinetic":[26],"equations":[27],"(nonlocal":[28],"in":[29,63],"velocity),":[30],"which":[31,53],"are":[32],"then":[33],"shown":[34],"characterize":[36],"all":[37],"with":[39],"finite":[40,68],"production.":[42],"Next,":[43],"we":[44],"prove":[45],"Liouville-type":[47],"theorem":[48],"for":[49,66],"genuinely":[50],"nonlinear":[51],"systems,":[52],"is":[54,74,81],"the":[55,59],"main":[56],"result":[57],"paper.":[60],"This":[61],"implies":[62],"particular":[64],"that":[65],"every":[67,71],"solution,":[70],"point":[72],"(t,x)\u2208R+\u00d7R\u2216J":[73],"vanishing":[76],"mean":[77],"oscillation,":[78],"where":[79],"J\u2282R+\u00d7R":[80],"set":[83],"Hausdorff":[85],"dimension":[86],"at":[87],"most":[88],"1.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-27T00:00:00"}