{"id":"https://openalex.org/W7214958747","doi":"https://doi.org/10.48550/arxiv.2609.37593","title":"Long time strong Sobolev instability for quasilinear NLS","display_name":"Long time strong Sobolev instability for quasilinear NLS","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214958747","doi":"https://doi.org/10.48550/arxiv.2609.37593"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37593","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37593","pdf_url":"https://arxiv.org/pdf/2609.37593","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/2609.37593","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133676881","display_name":"Yuri Cacchi\u00f2","orcid":"https://orcid.org/0000-0002-8605-7731","observed_orcids":["https://orcid.org/0000-0002-8605-7731"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cacchi\u00f2, Yuri","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080381250","display_name":"Filippo Giuliani","orcid":"https://orcid.org/0000-0003-1511-8311","observed_orcids":["https://orcid.org/0000-0003-1511-8311"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giuliani, Filippo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077401068","display_name":"Felice Iandoli","orcid":"https://orcid.org/0000-0001-8632-0547","observed_orcids":["https://orcid.org/0000-0001-8632-0547"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Iandoli, Felice","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5021963182","display_name":"Raffaele Scandone","orcid":"https://orcid.org/0000-0002-9105-878X","observed_orcids":["https://orcid.org/0000-0002-9105-878X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Scandone, Raffaele","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":1.0,"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":1.0,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0,"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":0.0,"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/quasilinear-schrodinger-equations","display_name":"quasilinear Schr\u00f6dinger equations","score":0.8610000014305115},{"id":"https://openalex.org/keywords/resonance-energy-transfer","display_name":"resonance energy transfer","score":0.8989999890327454},{"id":"https://openalex.org/keywords/paradifferential-calculus","display_name":"paradifferential calculus","score":0.968999981880188},{"id":"https://openalex.org/keywords/weak-turbulence","display_name":"weak turbulence","score":0.7760000228881836},{"id":"https://openalex.org/keywords/two-dimensional-torus","display_name":"two-dimensional torus","score":0.7110000252723694}],"concepts":[{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.7670999765396118},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6714000105857849},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5695000290870667},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.5630999803543091},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5601999759674072},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5353000164031982},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4993000030517578},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4756999909877777},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.45750001072883606},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4487000107765198},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.4255000054836273},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3928999900817871},{"id":"https://openalex.org/C2777952282","wikidata":"https://www.wikidata.org/wiki/Q3354606","display_name":"Transfer operator","level":2,"score":0.35040000081062317},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C106447425","wikidata":"https://www.wikidata.org/wiki/Q11379","display_name":"Energy transfer","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.28139999508857727},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2741999924182892},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37593","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37593","pdf_url":"https://arxiv.org/pdf/2609.37593","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.2609.37593","doi":"https://doi.org/10.48550/arxiv.2609.37593","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37593","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:2609.37593","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37593","pdf_url":"https://arxiv.org/pdf/2609.37593","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214958747.pdf","grobid_xml":"https://content.openalex.org/works/W7214958747.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2898046517","https://openalex.org/W4417283693","https://openalex.org/W2048745442","https://openalex.org/W2069360595","https://openalex.org/W4293879880","https://openalex.org/W2405744903","https://openalex.org/W2982908972","https://openalex.org/W4285787426","https://openalex.org/W4386240805","https://openalex.org/W4283452287"],"abstract_inverted_index":{"We":[0,118],"prove":[1],"long-time":[2],"strong":[3],"Sobolev":[4],"instability":[5,69],"for":[6,30,59],"a":[7,44,74,123,140,145,151],"class":[8],"of":[9,24,85,91,107,114,144],"quasilinear":[10,115,142],"Schr\u00f6dinger":[11],"equations":[12],"on":[13],"$\\mathbb":[14],"T^2$":[15],"arising,":[16],"via":[17],"the":[18,22,81,86,89,103,108,112],"Madelung":[19],"transform,":[20],"in":[21,88,111,157],"description":[23],"Euler-Korteweg":[25],"capillary":[26,158],"fluids.":[27,159],"More":[28],"precisely,":[29],"every":[31],"$s\\ge":[32],"7$,":[33],"arbitrarily":[34,38],"small":[35],"$\u03bc>0$,":[36],"and":[37,133,149],"large":[39],"$\\mathcal":[40],"K>0$,":[41],"we":[42,61],"construct":[43],"solution":[45],"such":[46],"that":[47],"$$":[48,53],"\\|u(0)\\|_{H^s}<\u03bc,":[49],"\\qquad":[50],"\\|u(T)\\|_{H^s}>\\mathcal":[51],"K":[52],"at":[54],"some":[55],"finite":[56],"time":[57,105],"$T$,":[58],"which":[60],"provide":[62],"an":[63],"explicit":[64],"exponential":[65],"upper":[66],"bound.":[67],"The":[68,93],"mechanism":[70],"is":[71,97],"generated":[72],"by":[73,121],"finite-dimensional":[75],"resonant":[76,146],"Toy":[77],"Model":[78],"associated":[79],"with":[80,128,153],"cubic":[82],"semilinear":[83],"part":[84],"equation,":[87],"spirit":[90],"Colliander-Keel-Staffilani-Takaoka-Tao.":[92],"main":[94],"technical":[95],"difficulty":[96],"to":[98],"justify":[99],"this":[100,120],"dynamics":[101,156],"over":[102],"long":[104],"scale":[106],"energy":[109,135],"transfer":[110],"presence":[113],"derivative":[116],"losses.":[117],"achieve":[119],"combining":[122],"weak":[124],"Birkhoff":[125],"normal":[126],"form":[127],"paradifferential":[129],"calculus,":[130],"microlocal":[131],"symmetrization,":[132],"modified":[134],"estimates.":[136],"Our":[137],"result":[138],"provides":[139],"rigorous":[141],"realization":[143],"energy-transfer":[147],"mechanism,":[148],"suggests":[150],"connection":[152],"weakly":[154],"turbulent":[155]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-01T00:00:00"}