{"id":"https://openalex.org/W7223708917","doi":"https://doi.org/10.48550/arxiv.2610.32180","title":"Well-posedness for the Cubic Nonlinear Schr\u00f6dinger Equation With Nonlinearity Supported on a Hypersurface","display_name":"Well-posedness for the Cubic Nonlinear Schr\u00f6dinger Equation With Nonlinearity Supported on a Hypersurface","publication_year":2026,"publication_date":"2026-10-23","ids":{"openalex":"https://openalex.org/W7223708917","doi":"https://doi.org/10.48550/arxiv.2610.32180"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.32180","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32180","pdf_url":"https://arxiv.org/pdf/2610.32180","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/2610.32180","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159651218","display_name":"Xilin Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I184565670","display_name":"Georgetown University","ror":"https://ror.org/05vzafd60","country_code":"US","type":"education","lineage":["https://openalex.org/I184565670"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chen, Xilin","raw_affiliation_strings":["Department of Mathematics & Statistics , Georgetown University , Washington , DC 20057 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics , Georgetown University , Washington , DC 20057 , USA","institution_ids":["https://openalex.org/I184565670"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5147347896","display_name":"Jianlei Huang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I184565670","display_name":"Georgetown University","ror":"https://ror.org/05vzafd60","country_code":"US","type":"education","lineage":["https://openalex.org/I184565670"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Huang, Jianlei","raw_affiliation_strings":["Department of Mathematics & Statistics , Georgetown University , Washington , DC 20057 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics , Georgetown University , Washington , DC 20057 , USA","institution_ids":["https://openalex.org/I184565670"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I184565670"],"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/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/cubic-nonlinear-schrodinger-equation","display_name":"cubic nonlinear Schr\u00f6dinger equation","score":0.9959999918937683},{"id":"https://openalex.org/keywords/well-posedness","display_name":"well-posedness","score":0.875},{"id":"https://openalex.org/keywords/anisotropic-sobolev-spaces","display_name":"anisotropic Sobolev spaces","score":0.9079999923706055},{"id":"https://openalex.org/keywords/global-well-posedness","display_name":"global well-posedness","score":0.8870000243186951},{"id":"https://openalex.org/keywords/local-well-posedness","display_name":"local well-posedness","score":0.9800000190734863}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7177000045776367},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6229000091552734},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5993000268936157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5910000205039978},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.5310999751091003},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.39660000801086426},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.3028999865055084},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29350000619888306},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2596000134944916}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.32180","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32180","pdf_url":"https://arxiv.org/pdf/2610.32180","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.2610.32180","doi":"https://doi.org/10.48550/arxiv.2610.32180","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.32180","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:2610.32180","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32180","pdf_url":"https://arxiv.org/pdf/2610.32180","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/W7223708917.pdf","grobid_xml":"https://content.openalex.org/works/W7223708917.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3019880789","https://openalex.org/W2193555673","https://openalex.org/W3183414141","https://openalex.org/W4224013641","https://openalex.org/W2021137228","https://openalex.org/W7120664919","https://openalex.org/W3199291462","https://openalex.org/W7114900814","https://openalex.org/W4281554927","https://openalex.org/W7053283897"],"abstract_inverted_index":{"We":[0,42],"prove":[1,27,44],"that":[2,28,45],"the":[3,29,46],"2-d":[4],"cubic":[5],"nonlinear":[6],"Schr\u00f6dinger":[7],"equation":[8,30,47],"with":[9,31,48],"nonlinearity":[10,33,50],"supported":[11],"on":[12],"a":[13,16],"line":[14],"or":[15],"sphere":[17],"is":[18,34,51],"globally":[19,52],"well-posed":[20,36,53],"in":[21,37,54],"\\(H^1(\\mathbb{R}^2)\\).":[22],"For":[23],"higher":[24],"dimensions,":[25],"we":[26],"hyperplane-supported":[32],"locally":[35],"suitable":[38],"anisotropic":[39],"Sobolev":[40],"spaces.":[41],"also":[43],"sphere-supported":[49],"\\(H^1(\\mathbb{R}^n)\\)":[55],"for":[56],"radial":[57],"data.":[58]},"counts_by_year":[],"updated_date":"2026-10-29T09:56:32.521200","created_date":"2026-10-27T00:00:00"}
