{"id":"https://openalex.org/W7204759286","doi":"https://doi.org/10.3934/math.20261098","title":"Maximal-time criteria for a generalized derivative nonlinear Schr\u00f6dinger equation","display_name":"Maximal-time criteria for a generalized derivative nonlinear Schr\u00f6dinger equation","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7204759286","doi":"https://doi.org/10.3934/math.20261098"},"language":"en","primary_location":{"id":"doi:10.3934/math.20261098","doi":"https://doi.org/10.3934/math.20261098","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.20261098","pdf_url":"http://www.aimspress.com/aimspress-data/math/2026/8/PDF/math-11-08-1098.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W7204759286"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://www.aimspress.com/aimspress-data/math/2026/8/PDF/math-11-08-1098.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043312790","display_name":"Senyue Luo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210151260","display_name":"Guangdong Open University","ror":"https://ror.org/054fysp39","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210151260"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Senyue Luo","raw_affiliation_strings":["Department of Basic Education , The Open University of Guangdong , Guangdong Polytechnic Institute , Guangzhou , Guangdong , 510091 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Education , The Open University of Guangdong , Guangdong Polytechnic Institute , Guangzhou , Guangdong , 510091 , China","institution_ids":["https://openalex.org/I4210151260"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084904589","display_name":"Meilan Qiu","orcid":"https://orcid.org/0000-0002-2407-9150","observed_orcids":["https://orcid.org/0000-0002-2407-9150"]},"institutions":[{"id":"https://openalex.org/I93477617","display_name":"Huizhou University","ror":"https://ror.org/03q3s7962","country_code":"CN","type":"education","lineage":["https://openalex.org/I93477617"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Meilan Qiu","raw_affiliation_strings":["School of Mathematics and Statistics , Huizhou University , Huizhou , Guangdong , 516007 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Huizhou University , Huizhou , Guangdong , 516007 , China","institution_ids":["https://openalex.org/I93477617"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111831248","display_name":"Zhiming Tan","orcid":"https://orcid.org/0009-0009-9788-1644","observed_orcids":["https://orcid.org/0009-0009-9788-1644"]},"institutions":[{"id":"https://openalex.org/I4210151260","display_name":"Guangdong Open University","ror":"https://ror.org/054fysp39","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210151260"]},{"id":"https://openalex.org/I93477617","display_name":"Huizhou University","ror":"https://ror.org/03q3s7962","country_code":"CN","type":"education","lineage":["https://openalex.org/I93477617"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiming Tan","raw_affiliation_strings":["Department of Basic Education, The Open University of Guangdong, Guangdong Polytechnic Institute, Guangzhou, Guangdong, 510091, China","School of Mathematics and Statistics, Huizhou University, Huizhou, Guangdong, 516007, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Education, The Open University of Guangdong, Guangdong Polytechnic Institute, Guangzhou, Guangdong, 510091, China","institution_ids":["https://openalex.org/I4210151260"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Huizhou University, Huizhou, Guangdong, 516007, China","institution_ids":["https://openalex.org/I93477617"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1200,"currency":"USD","value_usd":1200},"apc_paid":{"value":1200,"currency":"USD","value_usd":1200},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"8","first_page":"27448","last_page":"27467"},"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/derivative-nonlinear-schrodinger-equation","display_name":"derivative nonlinear Schr\u00f6dinger equation","score":0.9629999995231628},{"id":"https://openalex.org/keywords/blow-up-criterion","display_name":"blow-up criterion","score":0.6759999990463257},{"id":"https://openalex.org/keywords/blow-up-rate","display_name":"blow-up rate","score":0.6110000014305115},{"id":"https://openalex.org/keywords/energy-inequality","display_name":"energy inequality","score":0.7360000014305115},{"id":"https://openalex.org/keywords/homogeneous-dirichlet-boundary-conditions","display_name":"homogeneous Dirichlet boundary conditions","score":0.8119999766349792},{"id":"https://openalex.org/keywords/bounded-interval","display_name":"bounded interval","score":0.796999990940094},{"id":"https://openalex.org/keywords/local-existence","display_name":"local existence","score":0.48399999737739563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8192999958992004},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6697999835014343},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5889999866485596},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5295000076293945},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5163000226020813},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4966999888420105},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.49059998989105225},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.46160000562667847},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4097999930381775},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.365200012922287},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.36419999599456787},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.35679998993873596},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3255999982357025},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.28690001368522644},{"id":"https://openalex.org/C33257320","wikidata":"https://www.wikidata.org/wiki/Q1932744","display_name":"Second derivative","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.28110000491142273},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C99888217","wikidata":"https://www.wikidata.org/wiki/Q1288707","display_name":"Stopping time","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/math.20261098","doi":"https://doi.org/10.3934/math.20261098","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.20261098","pdf_url":"http://www.aimspress.com/aimspress-data/math/2026/8/PDF/math-11-08-1098.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/math.20261098","doi":"https://doi.org/10.3934/math.20261098","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.20261098","pdf_url":"http://www.aimspress.com/aimspress-data/math/2026/8/PDF/math-11-08-1098.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204759286.pdf","grobid_xml":"https://content.openalex.org/works/W7204759286.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1592146221","https://openalex.org/W1826826645","https://openalex.org/W1965664006","https://openalex.org/W1971735108","https://openalex.org/W1977635559","https://openalex.org/W1981543338","https://openalex.org/W1990258073","https://openalex.org/W2015961585","https://openalex.org/W2016037919","https://openalex.org/W2019167396","https://openalex.org/W2022028964","https://openalex.org/W2030768732","https://openalex.org/W2034648836","https://openalex.org/W2068457286","https://openalex.org/W2157662523","https://openalex.org/W2169431613","https://openalex.org/W2324756930","https://openalex.org/W2470228071","https://openalex.org/W2552874050","https://openalex.org/W2731494827","https://openalex.org/W2771373020","https://openalex.org/W4226525285","https://openalex.org/W4414770165","https://openalex.org/W7125149340"],"related_works":["https://openalex.org/W2324756930","https://openalex.org/W3184902134","https://openalex.org/W2470228071","https://openalex.org/W2963287935","https://openalex.org/W2077048138","https://openalex.org/W4400050740","https://openalex.org/W2731494827","https://openalex.org/W1558269687"],"abstract_inverted_index":{"We":[0],"study":[1],"a":[2,9,28,41,46,71,97],"generalized":[3],"derivative":[4],"nonlinear":[5],"Schr\u00f6dinger":[6],"equation":[7],"on":[8],"bounded":[10],"interval":[11],"under":[12],"homogeneous":[13],"Dirichlet":[14],"boundary":[15],"conditions.":[16],"Starting":[17],"from":[18],"the":[19,51,60,65,82,87,101,106],"local":[20,107],"$":[21,23,30,32,53,56,66,68,89,91],"H^2":[22,31,67,90],"well-posedness":[24],"theory,":[25],"we":[26],"derive":[27],"quantitative":[29,72],"energy":[33],"inequality":[34],"in":[35,84,100],"physical":[36],"space.":[37],"The":[38,93],"estimate":[39],"yields":[40],"genuine":[42],"continuation":[43],"criterion":[44],"at":[45],"finite":[47],"endpoint,":[48],"divergence":[49],"of":[50,86],"controlling":[52],"W^{1,":[54],"\\infty}":[55],"time":[57,62],"integral":[58],"whenever":[59],"maximal":[61],"is":[63,96,110],"finite,":[64],"blow-up":[69,74],"alternative,":[70],"lower":[73,79],"rate,":[75],"and":[76,116],"an":[77],"explicit":[78,113],"bound":[80],"for":[81],"lifespan":[83],"terms":[85],"initial":[88],"norm.":[92],"key":[94],"mechanism":[95],"derivative-loss":[98],"cancellation":[99],"highest-order":[102],"transport":[103],"term.":[104],"Thus,":[105],"existence":[108],"theory":[109],"supplemented":[111],"by":[112],"maximal-time":[114],"information":[115],"computable":[117],"growth":[118],"scales.":[119]},"counts_by_year":[],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2026-09-01T00:00:00"}