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

doi:10.1007/s10473-023-0319-9

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1333-1346.doi: 10.1007/s10473-023-0319-9

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

Xiaoguang You¹, Aibin Zang²

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;

收稿日期:2021-11-18 修回日期:2022-03-11 出版日期:2023-06-25 发布日期:2023-06-06
作者简介:Xiaoguang You, E-mail: wiliam_you@aliyun.com;Aibin Zang, E-mail: zangab05@126.com
基金资助:
Aibin Zang was supported partially by the National Natural Science Foundation of China (11771382, 12061080, 12261093) and the Jiangxi Provincial Natural Science Foundation (20224ACB201004).

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

Xiaoguang You¹, Aibin Zang²

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).

摘要/Abstract

摘要： 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.

关键词: second-grade fluid equations, Euler equations, exterior domain, singular limit

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

Xiaoguang You, Aibin Zang. THE SINGULAR LIMIT OF SECOND-GRADE FLUID EQUATIONS IN A 2D EXTERIOR DOMAIN^*[J]. 数学物理学报(英文版), 2023, 43(3): 1333-1346.

Xiaoguang You, Aibin Zang. THE SINGULAR LIMIT OF SECOND-GRADE FLUID EQUATIONS IN A 2D EXTERIOR DOMAIN^*[J]. Acta mathematica scientia,Series B, 2023, 43(3): 1333-1346.

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

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

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