This paper is concerned with the monotonicity and convexity of the incompressible rotational cavity flow past a fixed obstacle. More precisely, we first establish the single intersection property of the free boundary by the Serrin's under–over theorem, and prove the monotonicity of the free boundary with respect to the obstacle. If the obstacle is concave to the fluid, it is proved that the free boundary is convex to the fluid.

中文翻译：

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不可压缩旋转腔流的单调性和凸性

本文关注经过固定障碍物的不可压缩旋转空腔流的单调性和凸性。更准确地说，我们首先通过Serrin下-上定理建立了自由边界的单交性质，并证明了自由边界相对于障碍物的单调性。如果障碍物相对于流体是凹的，则证明自由边界相对于流体是凸的。