Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (3): 1333-1346.doi: 10.1007/s10473-023-0319-9

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THE SINGULAR LIMIT OF SECOND-GRADE FLUID EQUATIONS IN A 2D EXTERIOR DOMAIN*

Xiaoguang You1, Aibin Zang2   

  1. 1. School of Mathematics, Northwest University, Xi'an 710069, China;
    2. School of Mathematics and Computer Science & The Center of Applied Mathematics, Yichun University, Yichun 336000, China;
  • Received:2021-11-18 Revised:2022-03-11 Online:2023-06-25 Published:2023-06-06
  • About author:Xiaoguang You, E-mail: wiliam_you@aliyun.com;Aibin Zang, E-mail: zangab05@126.com
  • Supported by:
    Aibin Zang was supported partially by the National Natural Science Foundation of China (11771382, 12061080, 12261093) and the Jiangxi Provincial Natural Science Foundation (20224ACB201004).

Abstract: In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a well-known non-Newtonian fluid model, with two parameters: $\alpha$, which represents the length-scale, while $\nu > 0$ corresponds to the viscosity. We prove that, as $\nu, \alpha$ tend to zero, the solution of the second-grade fluid equations with suitable initial data converges to the one of Euler equations, provided that $\nu = {o}(\alpha^\frac{4}{3})$. Moreover, the convergent rate is obtained.

Key words: second-grade fluid equations, Euler equations, exterior domain, singular limit

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