Fluid flows around an obstacle generate vortices which are difficult to locate and to describe. A variational formulation for a class of mixed and nonstandard boundary conditions on a smooth obstacle is discussed for the Stokes equations. Possible boundary data are then derived through separation of variables of biharmonic equations in a planar region having an internal concave corner. Explicit singular solutions show that, at least qualitatively, these conditions are able to reproduce vortices over the leeward wall of the obstacle.

中文翻译：

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平面Stokes方程在凹角附近引起涡旋的边界条件

障碍物周围的流体流动会产生难以定位和描述的涡流。针对斯托克斯方程，讨论了光滑障碍物上一类混合和非标准边界条件的变分公式。然后，通过在具有内部凹角的平面区域中分离双调和方程变量来导出可能的边界数据。明确的奇异解表明，至少在质量上，这些条件能够在障碍物的背风壁上复制漩涡。