{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T07:15:39Z","timestamp":1783149339805,"version":"3.54.6"},"reference-count":35,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100021171","name":"Basic and Applied Basic Research Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2026A1515012141"],"award-info":[{"award-number":["2026A1515012141"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100017610","name":"Shenzhen Science and Technology Innovation Program","doi-asserted-by":"publisher","award":["JCYJ20240813151513017"],"award-info":[{"award-number":["JCYJ20240813151513017"]}],"id":[{"id":"10.13039\/501100017610","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFA1010300"],"award-info":[{"award-number":["2023YFA1010300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2025T180840"],"award-info":[{"award-number":["2025T180840"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2024M760057"],"award-info":[{"award-number":["2024M760057"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics Letters"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.aml.2026.109996","type":"journal-article","created":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T09:57:38Z","timestamp":1778579858000},"page":"109996","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Sharp decay rates of large solutions for the incompressible Phan-Thien\u2013Tanner model in R3"],"prefix":"10.1016","volume":"181","author":[{"given":"Yuhui","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0722-9097","authenticated-orcid":false,"given":"Minling","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zheng-an","family":"Yao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"4","key":"10.1016\/j.aml.2026.109996_b1","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/0377-0257(77)80021-9","article-title":"A new constitutive equation derived from network theory","volume":"2","author":"Phan-Thien","year":"1977","journal-title":"J. Non-Newton. Fluid Mech."},{"issue":"3","key":"10.1016\/j.aml.2026.109996_b2","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1122\/1.549481","article-title":"A nonlinear network viscoelastic model","volume":"22","author":"Phan-Thien","year":"1978","journal-title":"J. Rheol."},{"issue":"5","key":"10.1016\/j.aml.2026.109996_b3","doi-asserted-by":"crossref","first-page":"4537","DOI":"10.1137\/21M1435161","article-title":"Sharp rates of decay and global-in-time stability of large solutions to the three-dimensional incompressible Phan-Thien\u2013Tanner system of polymeric flows","volume":"55","author":"Chen","year":"2023","journal-title":"SIAM J. Math. Anal."},{"issue":"9","key":"10.1016\/j.aml.2026.109996_b4","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/0362-546X(90)90097-Z","article-title":"Existence results for the flow of viscoelastic fluids with a differential constitutive law","volume":"15","author":"Guillop\u00e9","year":"1990","journal-title":"Nonlinear Anal."},{"issue":"3","key":"10.1016\/j.aml.2026.109996_b5","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1051\/m2an\/1990240303691","article-title":"Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type","volume":"24","author":"Guillop\u00e9","year":"1990","journal-title":"RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r."},{"issue":"1","key":"10.1016\/j.aml.2026.109996_b6","first-page":"1","article-title":"Some theoretical results concerning non-Newtonian fluids of the Oldroyd kind","volume":"26","author":"Fern\u00e1ndez-Cara","year":"1998","journal-title":"Ann. Sc. Norm. Sup. Pisa Cl. Sci."},{"issue":"1","key":"10.1016\/j.aml.2026.109996_b7","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1137\/S0036141099359317","article-title":"About lifespan of regular solutions of equations related to viscoelastic fluids","volume":"33","author":"Chemin","year":"2001","journal-title":"SIAM J. Math. Anal."},{"issue":"2","key":"10.1016\/j.aml.2026.109996_b8","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1016\/j.jde.2009.07.011","article-title":"Remarks on the blowup criteria for oldroyd models","volume":"248","author":"Lei","year":"2010","journal-title":"J. Differential Equations"},{"issue":"11","key":"10.1016\/j.aml.2026.109996_b9","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1002\/cpa.20074","article-title":"On hydrodynamics of viscoelastic fluids","volume":"58","author":"Lin","year":"2005","journal-title":"Comm. Pure Appl. Math."},{"issue":"3","key":"10.1016\/j.aml.2026.109996_b10","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s00021-019-0446-1","article-title":"Global well-posedness in the critical Besov spaces for the incompressible Oldroyd-B model without damping mechanism","volume":"21","author":"Chen","year":"2019","journal-title":"J. Math. Fluid Mech."},{"key":"10.1016\/j.aml.2026.109996_b11","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.jde.2023.06.003","article-title":"Global strong solutions and large time behavior to a micro-macro model for compressible polymeric fluids near equilibrium","volume":"370","author":"Deng","year":"2023","journal-title":"J. Differential Equations"},{"issue":"5","key":"10.1016\/j.aml.2026.109996_b12","doi-asserted-by":"crossref","first-page":"2815","DOI":"10.1137\/120892350","article-title":"Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows","volume":"45","author":"Hu","year":"2013","journal-title":"SIAM J. Math. Anal."},{"issue":"3","key":"10.1016\/j.aml.2026.109996_b13","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s00205-007-0089-x","article-title":"Global solutions for incompressible viscoelastic fluids","volume":"188","author":"Lei","year":"2008","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"4","key":"10.1016\/j.aml.2026.109996_b14","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1002\/cpa.20219","article-title":"On the initial\u2013boundary value problem of the incompressible viscoelastic fluid system","volume":"61","author":"Lin","year":"2008","journal-title":"Comm. Pure Appl. Math."},{"issue":"4","key":"10.1016\/j.aml.2026.109996_b15","doi-asserted-by":"crossref","first-page":"2266","DOI":"10.1137\/110851742","article-title":"Global existence of strong solution for equations related to the incompressible viscoelastic fluids in the critical Lp framework","volume":"44","author":"Zhang","year":"2012","journal-title":"SIAM J. Math. Anal."},{"issue":"2","key":"10.1016\/j.aml.2026.109996_b16","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1063\/5.0010742","article-title":"Global solutions to the n-dimensional incompressible Oldroyd-B model without damping mechanism","volume":"62","author":"Zhai","year":"2021","journal-title":"J. Math. Phys."},{"issue":"7","key":"10.1016\/j.aml.2026.109996_b17","doi-asserted-by":"crossref","first-page":"2039","DOI":"10.1016\/j.jfa.2017.09.002","article-title":"Global small solutions of 3D incompressible Oldroyd-B model without damping mechanism","volume":"274","author":"Zhu","year":"2018","journal-title":"J. Funct. Anal."},{"issue":"3","key":"10.1016\/j.aml.2026.109996_b18","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1088\/1361-6544\/aaeec7","article-title":"Optimal decay rates for solutions to the incompressible Oldroyd-B model in R3","volume":"32","author":"Hieber","year":"2019","journal-title":"Nonlinearity"},{"key":"10.1016\/j.aml.2026.109996_b19","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.jde.2024.01.016","article-title":"Global existence and decay rates of solutions to the Oldroyd-B model with stress tensor diffusion","volume":"389","author":"Huang","year":"2024","journal-title":"J. Differential Equations"},{"key":"10.1016\/j.aml.2026.109996_b20","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.jde.2021.10.046","article-title":"Optimal time-decay estimates for an Oldroyd-B model with zero viscosity","volume":"306","author":"Huang","year":"2022","journal-title":"J. Differential Equations"},{"issue":"2","key":"10.1016\/j.aml.2026.109996_b21","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1017\/prm.2022.2","article-title":"The Cauchy problem for an inviscid Oldroyd-B model in three dimensions: global well posedness and optimal decay rates","volume":"153","author":"Liu","year":"2023","journal-title":"Proc. Roy. Soc. Edinburgh Sect. A"},{"key":"10.1016\/j.aml.2026.109996_b22","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.nonrwa.2024.104100","article-title":"The Cauchy problem for an inviscid and non-diffusive Oldroyd-B model in two dimensions","volume":"79","author":"Tu","year":"2024","journal-title":"Nonlinear Anal. Real World Appl."},{"issue":"1","key":"10.1016\/j.aml.2026.109996_b23","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1142\/S0218202520500049","article-title":"The Cauchy problem for an Oldroyd-B model in three dimensions","volume":"30","author":"Wang","year":"2020","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"4","key":"10.1016\/j.aml.2026.109996_b24","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1016\/j.jde.2018.04.003","article-title":"Global well-posedness and decay rates for the three dimensional compressible Oldroyd-B model","volume":"265","author":"Zhou","year":"2018","journal-title":"J. Differential Equations"},{"issue":"2","key":"10.1016\/j.aml.2026.109996_b25","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1142\/S0252959900000170","article-title":"Global solutions for some Oldroyd models of non-Newtonian flows","volume":"21","author":"Lions","year":"2000","journal-title":"Chin. Ann. Math. Ser. B"},{"issue":"3","key":"10.1016\/j.aml.2026.109996_b26","first-page":"348","article-title":"Global existence of large data weak solutions for a simplified compressible Oldroyd-B model without stress diffusion","volume":"36","author":"Lu","year":"2020","journal-title":"Anal. Theory Appl."},{"issue":"1","key":"10.1016\/j.aml.2026.109996_b27","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1137\/17M1128654","article-title":"Relative entropy, weak-strong uniqueness, and conditional regularity for a compressible Oldroyd-B model","volume":"50","author":"Lu","year":"2018","journal-title":"SIAM J. Math. Anal."},{"issue":"2","key":"10.1016\/j.aml.2026.109996_b28","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1137\/15M1037020","article-title":"Global solutions to the Oldroyd-B model with a class of large initial data","volume":"48","author":"Fang","year":"2016","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/j.aml.2026.109996_b29","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.jde.2021.02.020","article-title":"Strong solutions of the equations for viscoelastic fluids in some classes of large data","volume":"282","author":"Jiang","year":"2021","journal-title":"J. Differential Equations"},{"issue":"5","key":"10.1016\/j.aml.2026.109996_b30","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1016\/j.matpur.2011.04.008","article-title":"Global existence of weak solutions to macroscopic models of polymeric flows","volume":"96","author":"Masmoudi","year":"2011","journal-title":"J. Math. Pures Appl."},{"issue":"11","key":"10.1016\/j.aml.2026.109996_b31","doi-asserted-by":"crossref","first-page":"6758","DOI":"10.1016\/j.jde.2019.07.005","article-title":"Blow up and global existence for the periodic Phan-Thein\u2013Tanner model","volume":"267","author":"Chen","year":"2019","journal-title":"J. Differential Equations"},{"issue":"4","key":"10.1016\/j.aml.2026.109996_b32","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1142\/S0219530522500051","article-title":"Global existence and optimal time decay rates for the three-dimensional incompressible Phan-Thien\u2013Tanner model","volume":"21","author":"Chen","year":"2023","journal-title":"Anal. Appl. (Singap.)"},{"issue":"9","key":"10.1016\/j.aml.2026.109996_b33","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1088\/1361-6544\/ad6b6f","article-title":"Global solutions to the three-dimensional inhomogeneous incompressible Phan-Thien\u2013Tanner system with a class of large initial data","volume":"37","author":"Chen","year":"2024","journal-title":"Nonlinearity"},{"issue":"3\u20134","key":"10.1016\/j.aml.2026.109996_b34","first-page":"451","article-title":"The sharp time decay rates and stability of large solutions to the two-dimensional Phan-Thien\u2013Tanner system with magnetic field","volume":"129","author":"Chen","year":"2022","journal-title":"Asymptot. Anal."},{"issue":"2","key":"10.1016\/j.aml.2026.109996_b35","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1007\/s00205-014-0732-2","article-title":"Global solution to the incompressible Oldroyd-B model in the critical Lp framework: The case of the non-small coupling parameter","volume":"213","author":"Zi","year":"2014","journal-title":"Arch. Ration. Mech. Anal."}],"container-title":["Applied Mathematics Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965926001278?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965926001278?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T06:21:55Z","timestamp":1783146115000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0893965926001278"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":35,"alternative-id":["S0893965926001278"],"URL":"https:\/\/doi.org\/10.1016\/j.aml.2026.109996","relation":{},"ISSN":["0893-9659"],"issn-type":[{"value":"0893-9659","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Sharp decay rates of large solutions for the incompressible Phan-Thien\u2013Tanner model in","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics Letters","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.aml.2026.109996","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"109996"}}