Global well-posedness and inviscid limits of the generalized Oldroyd type models

作者：Zhai, Xiaoping; Dan, Yuanyuan^*; Li, Yongsheng

来源：NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2022, 63: 103414.

DOI：10.1016/j.nonrwa.2021.103414

• Global solutions
• Oldroyd-B model
• Inviscid limit
• Besov space

We obtain the global small solutions to the generalized Oldroyd-B model without damping on the stress tensor in Rn. 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 Tau, 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.

• 单位
  广东金融学院