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

Abstract

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

17pages

References in corpus (1)

• Optimal decay for the $n$-dimensional incompressible Oldroyd-B model without damping mechanism

Cited by in corpus (2)

• Global Regularity and instability for the incompressible non-viscous Oldroyd-B model
• Global well-posedness, stability and instability for the non-viscous Oldroyd-B model