We consider a 2D vorticity configuration where vorticity is highly concentrated around a curve and exponentially decaying away from it: the intensity of the vorticity is O(1/ε) on the curve while it decays on an O(ε) distance from the curve itself. We prove that, if the initial datum is of vortex‐layer type, Euler solutions preserve this structure for a time that does not depend on ε. Moreover, the motion of the center of the layer is well approximated by the Birkhoff‐Rott equation. © 2020 Wiley Periodicals, Inc.

中文翻译：

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小涡旋层

我们考虑二维涡度配置，其中涡度高度集中在曲线周围，并从其呈指数衰减：涡度在曲线上的强度为O（1 / ε），而在距曲线本身O（ε）距离处衰减。我们证明，如果初始基准面是涡旋层类型，则欧拉解在不依赖ε的时间内保留该结构。此外，通过Birkhoff-Rott方程可以很好地近似层中心的运动。©2020 Wiley Periodicals，Inc.