In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity \(\Omega \), such that it has positive vorticity and is concentrated in a finite disjoint union of smooth curves with finite length is the trivial one: constant vorticity amplitude supported on a union of nested, concentric circles. The proof follows a desingularization argument and a calculus of variations flavor.

中文翻译：

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关于静止和匀速旋转涡流片的备注：刚性结果

在本文中，我们证明了涡片方程的唯一解，无论是静止的还是以负角速度\(\Omega \)匀速旋转，这样它都具有正涡度，并且集中在光滑曲线的有限不相交联合中有限长度是微不足道的：由嵌套的同心圆联合支撑的恒定涡量振幅。证明遵循去奇异化论证和变体演算。