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

2021/06/28 by Xiaoping Zhai, Zhai, Xiaoping, Yuanyuan Dan +3 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2106.14785

openalex publication_date 2021/06/28 · openalex created_date 2021/07/05 · openalex updated_date 2026/07/28

Abstract

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 [J Differ Equ 259:1958--1966, 2015)]. 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.

Citations

• Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type

Cited by

• Global Regularity and instability for the incompressible non-viscous Oldroyd-B model

Related

• Global well-posedness and large time behavior for the Oldroyd-B model
• Global regularity and large time behavior for some inviscid Oldroyd-B models in ℝ²
• Global well-posedness and uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model
• Global existence and optimal decay of solutions to the incompressible Oldroyd-B model with only stress tensor dissipation and without damping mechanism
• Global well-posedness, stability and instability for the non-viscous Oldroyd-B model