In this note we investigate the asymptotic behavior of plane shear thickening fluids around a bounded obstacle. Different from the Navier–Stokes case considered by Gilbarg–Weinberger in Gilbarg and Weinberger (Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5(2):381-404, 1978), where the good structure of the vorticity can be exploited and weighted energy estimates can be applied, we have to overcome the nonlinear term of high order. The decay estimates of the velocity was obtained by combining Point-wise Behavior Theorem in Galdi (An Introduction to the Mathematical Theory of the Navier–Stokes Equations Springer, New York, 2011) and Brezis–Gallouet inequality in Brezis and Gallouet (Nonlinear Anal. 4(4):677-681, 1980) together, which is independent of interest.

中文翻译：

---

有界能量积分的平面剪切增稠流体的渐近性质

在本文中，我们研究了有界障碍物周围的平面剪切增稠流体的渐近行为。与Gilbarg–Weinberger在Gilbarg和Weinberger中所考虑的Navier–Stokes案例不同（Ann。Scuola Norm。Sup。Pisa Cl。Sci。（4）5（2）：381-404，1978），可以利用涡度并可以应用加权能量估计，我们必须克服高阶的非线性项。速度的衰减估计值是通过结合Galdi中的逐点行为定理（Navier-Stokes方程数学理论导论，Springer，纽约，2011年）和Brezis和Gallouet中的Brezis-Gallouet不等式（非线性分析）来获得的。 4（4）：677-681，1980），这与利益无关。