Global well-posedness and inviscid limits of the generalized Oldroyd type models. (February 2022)

• Record Type: Journal Article
• Authors: Zhai, Xiaoping; Dan, Yuanyuan; Li, Yongsheng
• Is Part Of: Nonlinear analysis. Volume 63(2022)
• Publication Date: 2022-02
• Subjects: Global solutions -- Oldroyd-B model -- Inviscid limit -- Besov space; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103414
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We obtain the global small solutions to the generalized Oldroyd-B model without damping on the stress tensor in R n . Our result give positive answers partially to the question proposed by Elgindi and Liu (Remark 2 in Elgindi and Liu (2015)). The proof relies heavily on the trick of transferring dissipation from u to τ, and a new commutator estimate which may be of interest for future works. Moreover, we prove a global result of inviscid limit of two dimensional Oldroyd type models in the Sobolev spaces. The convergence rate is also obtained simultaneously.