We consider the equations of a rotating incompressible non-Newtonian fluid flow of grade two in a three dimensional torus. We prove two different results of global existence of strong solutions. In the first case, we consider that the elasticity coefficient α is arbitrary and we suppose that the third components of the vertical average of the initial data and of the forcing term are small compared to the horizontal components. In the second case, we consider a forcing term and initial data of arbitrary size but we restrict the size of α. In both cases, we show that the limit system is composed of a linear system and a second grade fluid system with two variables and three components.

中文翻译：

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3D旋转二级流体系统的全球存在

我们考虑了三维圆环中二级不可旋转的非牛顿流体旋转方程。我们证明了强有力的解决方案在全球存在的两种不同结果。在第一种情况下，我们认为弹性系数α是任意的，并且假定初始数据和强迫项的垂直平均值的第三分量比水平分量小。在第二种情况下，我们考虑强迫项和任意大小的初始数据，但我们限制了α的大小。在这两种情况下，我们都表明极限系统由线性系统和具有两个变量和三个分量的二级流体系统组成。