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

doi:10.1007/s10473-023-0319-9

Abstract

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].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^*

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