{"id":"https://openalex.org/W7220716055","doi":"https://doi.org/10.48550/arxiv.2610.05802","title":"Scattering of non-radial solutions for the fourth-order Schr\u00f6dinger equation with $\\dot{H}^{1/2}$-critical and supercritical nonlinearity","display_name":"Scattering of non-radial solutions for the fourth-order Schr\u00f6dinger equation with $\\dot{H}^{1/2}$-critical and supercritical nonlinearity","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220716055","doi":"https://doi.org/10.48550/arxiv.2610.05802"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05802","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05802","pdf_url":"https://arxiv.org/pdf/2610.05802","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.05802","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035317620","display_name":"Takahisa Inui","orcid":"https://orcid.org/0000-0001-9951-3890","observed_orcids":["https://orcid.org/0000-0001-9951-3890"]},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"The University of Osaka","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Inui, Takahisa","raw_affiliation_strings":["Department of Mathematics , Graduate School of Science , The University of Osaka , Japan 560-0043"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Graduate School of Science , The University of Osaka , Japan 560-0043","institution_ids":["https://openalex.org/I98285908"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153480550","display_name":"Koichi Komada","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Komada, Koichi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108667986","display_name":"Kuranosuke Nishimura","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]},{"id":"https://openalex.org/I4405285833","display_name":"Waseda Research Institute for Science and Engineering","ror":"https://ror.org/00dqvpt71","country_code":"JP","type":"facility","lineage":["https://openalex.org/I150744194","https://openalex.org/I4405285833"]},{"id":"https://openalex.org/I98285908","display_name":"The University of Osaka","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Nishimura, Kuranosuke","raw_affiliation_strings":["Department of Mathematics , Graduate School of Science , The University of Osaka , Japan 560-0043","Research Institute for Science and Engineering , Waseda University , Japan 169-8555"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Graduate School of Science , The University of Osaka , Japan 560-0043","institution_ids":["https://openalex.org/I98285908"]},{"raw_affiliation_string":"Research Institute for Science and Engineering , Waseda University , Japan 169-8555","institution_ids":["https://openalex.org/I150744194","https://openalex.org/I4405285833"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":9.999999747378752e-05,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.0,"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/fourth-order-schrodinger-equation","display_name":"fourth-order Schr\u00f6dinger equation","score":0.9240000247955322},{"id":"https://openalex.org/keywords/nonradial-solutions","display_name":"non-radial solutions","score":0.8199999928474426},{"id":"https://openalex.org/keywords/scattering-theory","display_name":"scattering theory","score":0.7879999876022339},{"id":"https://openalex.org/keywords/focusing-nonlinearity","display_name":"focusing nonlinearity","score":0.8220000267028809},{"id":"https://openalex.org/keywords/supercritical-nonlinearity","display_name":"supercritical nonlinearity","score":0.843999981880188},{"id":"https://openalex.org/keywords/critical-nonlinearity","display_name":"critical nonlinearity","score":0.7929999828338623},{"id":"https://openalex.org/keywords/concentration-compactness","display_name":"concentration compactness","score":0.7950000166893005},{"id":"https://openalex.org/keywords/virial-identity","display_name":"virial identity","score":0.9779999852180481}],"concepts":[{"id":"https://openalex.org/C189549420","wikidata":"https://www.wikidata.org/wiki/Q620602","display_name":"Virial theorem","level":3,"score":0.7991999983787537},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.6664000153541565},{"id":"https://openalex.org/C93218973","wikidata":"https://www.wikidata.org/wiki/Q7934790","display_name":"Virial coefficient","level":2,"score":0.635200023651123},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6248000264167786},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6205000281333923},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.5819000005722046},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.51419997215271},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.47749999165534973},{"id":"https://openalex.org/C118419359","wikidata":"https://www.wikidata.org/wiki/Q682585","display_name":"Supercritical fluid","level":2,"score":0.477400004863739},{"id":"https://openalex.org/C53810900","wikidata":"https://www.wikidata.org/wiki/Q214967","display_name":"Equation of state","level":2,"score":0.4431000053882599},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44190001487731934},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42250001430511475},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.4154999852180481},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.38119998574256897},{"id":"https://openalex.org/C67105901","wikidata":"https://www.wikidata.org/wiki/Q903737","display_name":"Scattering theory","level":3,"score":0.3517000079154968},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.34929999709129333},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.34709998965263367},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.31290000677108765},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3052000105381012},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2538999915122986},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.2533999979496002},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2529999911785126}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05802","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05802","pdf_url":"https://arxiv.org/pdf/2610.05802","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.2610.05802","doi":"https://doi.org/10.48550/arxiv.2610.05802","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05802","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:2610.05802","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05802","pdf_url":"https://arxiv.org/pdf/2610.05802","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/G9000374285","display_name":null,"funder_award_id":"JPMJMS25A5","funder_id":"https://openalex.org/F4320338247","funder_display_name":"Moonshot Research and Development Program"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320338247","display_name":"Moonshot Research and Development Program","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220716055.pdf","grobid_xml":"https://content.openalex.org/works/W7220716055.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7214730453","https://openalex.org/W7214766192"],"related_works":["https://openalex.org/W7080129916","https://openalex.org/W2998971662","https://openalex.org/W2077663392","https://openalex.org/W2085382681","https://openalex.org/W2736499214","https://openalex.org/W7138429631","https://openalex.org/W2951283401","https://openalex.org/W2002823123","https://openalex.org/W7214730453","https://openalex.org/W4220771382"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,39,51,68,73,79,83,104,115,120,124,128,142,145],"focusing":[3],"nonlinear":[4],"fourth-order":[5],"Schr\u00f6dinger":[6],"equation":[7],"\\begin{equation*}":[8],"i":[9],"\\partial_t":[10],"u":[11,16],"+":[12,59,65,91,97,136],"\u03bc\u0394u":[13],"-":[14,18],"\u0394^2":[15],"=":[17],"|u|^{p-1}":[19],"u,":[20],"\\":[21,22,23],"(t,x)":[24],"\\in":[25],"\\mathbb{R}":[26],"\\times":[27],"\\mathbb{R}^d,":[28],"\\end{equation*}":[29],"where":[30,53,85],"$\u03bc\\ge":[31],"0$.":[32],"The":[33,131],"scattering":[34,74],"of":[35,75,144],"radial":[36],"solutions":[37,77],"below":[38,78],"ground":[40,80],"state":[41,81],"is":[42,101,138],"shown":[43],"by":[44,108],"Guo":[45],"(2016)":[46],"and":[47,57,89],"Dinh":[48],"(2021)":[49],"in":[50,82,114,123,147],"case":[52,84],"$d":[54,86],"\\ge":[55,87,134],"2$":[56,88],"$1":[58,90],"8/d":[60],"<":[61,63,95],"p":[62,94],"1":[64,96,135],"8/(d-4)_{+}$.":[66,98],"In":[67],"present":[69],"paper,":[70],"we":[71,118],"prove":[72],"non-radial":[76,116],"8/(d-1)":[92],"\\le":[93],"Our":[99],"proof":[100],"based":[102],"on":[103],"concentration":[105],"compactness":[106],"argument":[107],"Kenig--Merle":[109],"(2006).":[110],"To":[111],"overcome":[112],"difficulties":[113],"case,":[117],"use":[119],"virial":[121,149],"identity":[122],"direction":[125],"orthogonal":[126],"to":[127,140],"momentum":[129],"vector.":[130],"condition":[132],"$p":[133],"8/(d-1)$":[137],"required":[139],"show":[141],"positivity":[143],"functional":[146],"that":[148],"identity.":[150]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
