{"title":"Global solutions of the 3D incompressible inhomogeneous viscoelastic system","authors":"Chengfei Ai , Yong Wang","doi":"10.1016/j.na.2025.113747","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we prove the global existence of strong solutions for the 3D incompressible inhomogeneous viscoelastic system. We avoid to use the “initial state” assumption and the “div–curl” structure in the proof of global solutions inspired by the works (Zhu,2018; Zhu,2022). It is a key to transform the original system into a suitable dissipative system by introducing a new effective tensor, which is useful to establish a series of energy estimates with appropriate time weights.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"254 ","pages":"Article 113747"},"PeriodicalIF":1.3000,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X25000021","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we prove the global existence of strong solutions for the 3D incompressible inhomogeneous viscoelastic system. We avoid to use the “initial state” assumption and the “div–curl” structure in the proof of global solutions inspired by the works (Zhu,2018; Zhu,2022). It is a key to transform the original system into a suitable dissipative system by introducing a new effective tensor, which is useful to establish a series of energy estimates with appropriate time weights.
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