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 [J Differ Equ 259:1958-1966]. 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.

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