We obtain the global small solutions to the generalized Oldroyd-B model without damping on the stress tensor in ${\mathbb{R}}^n$. 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 $\tau$, 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.

中文翻译：

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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 ${\mathbb{电阻}}^n$. 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$你$ 到 $\tau$，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。