When a liquid fills the semi-infinite space between two concentric cylinders which rotate at different steady speeds, how about the shape of the free surface on top of the fluid? The different fluids will lead to a different shape. For the Newtonian fluid, the meniscus descends due to the centrifugal forces. However, for the certain non-Newtonian fluid, the meniscus climbs the internal cylinder. We want to explain the above phenomenon by a rigorous mathematical analysis theory. In the present paper, as the first step, we focus on the Newtonian fluid. This is a steady free boundary problem. We aim to establish the well-posedness of this problem. Furthermore, we prove the convergence of the formal perturbation series obtained by Joseph and Fosdick in Arch. Ration. Mech. Anal. 49 (1973), 321–380.

当液体充满两个以不同稳定速度旋转的同心圆柱体之间的半无限空间时，流体顶部的自由表面的形状如何？不同的流体将导致不同的形状。对于牛顿流体，弯月面由于离心力而下降。然而，对于某些非牛顿流体，弯月面会爬上内圆柱。我们想用严谨的数学分析理论来解释上述现象。在本文中，作为第一步，我们关注牛顿流体。这是一个稳定的自由边界问题。我们的目标是确定这个问题的适定性。此外，我们证明了 Joseph 和 Fosdick 在 Arch 中获得的形式扰动级数的收敛性。配给。机甲。肛门。49 (1973), 321–380。