Nonlinear Analysis: Real World Applications ( IF 1.8 ) Pub Date : 2021-09-08 , DOI: 10.1016/j.nonrwa.2021.103414 Xiaoping Zhai 1 , Yuanyuan Dan 2, 3 , Yongsheng Li 3
We obtain the global small solutions to the generalized Oldroyd-B model without damping on the stress tensor in . 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 to , 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.
中文翻译:
广义 Oldroyd 型模型的全局适定性和无粘性极限
我们获得了广义 Oldroyd-B 模型的全局小解,而不会对应力张量产生阻尼 . 我们的结果部分地对 Elgindi 和 Liu 提出的问题给出了肯定的回答(Elgindi 和 Liu(2015)中的备注 2)。证明在很大程度上依赖于将耗散从 到 ,以及可能对未来工作感兴趣的新换向器估计。此外,我们证明了 Sobolev 空间中二维 Oldroyd 型模型的无粘性极限的全局结果。收敛速度也是同时获得的。