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.
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
.
DOI: 10.1007/s10473-023-0319-9
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