SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5363-5388, January 2020.
In this paper, we consider steady Euler flows in a planar bounded domain in which the vorticity is sharply concentrated in a finite number of disjoint regions of small diameter. Such flows are closely related to the point vortex model and can be regarded as desingularization of point vortices. By an adaption of the vorticity method, we construct a family of steady Euler flows in which the vorticity is concentrated near a global minimum point of the Robin function of the domain, and the corresponding stream function satisfies a semilinear elliptic equation with a given profile function. Furthermore, for any given isolated minimum point ($x_1,\ldots,x_k$) of the Kirchhoff--Routh function of the domain, we prove that there exists a family of steady Euler flows whose vorticity is supported in $k$ small regions near $x_i$, and near each $x_i$ the corresponding stream function satisfies a semilinear elliptic equation with a given profile function.

中文翻译：

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通过涡度法对二维稳态欧拉流的涡旋进行反奇异化

SIAM数学分析杂志，第52卷，第6期，第5363-5388页，2020年1月。
在本文中，我们考虑在平面有界域中的稳定欧拉流，其中涡旋急剧集中在有限数量的小直径不相交区域中。这样的流动与点涡模型密切相关，可以看作是点涡的去奇化。通过采用涡度方法，我们构建了一个稳定的欧拉流族，其中涡度集中在域的Robin函数的全局最小点附近，并且相应的流函数满足具有给定轮廓函数的半线性椭圆方程。此外，对于该域的Kirchhoff-Routh函数的任何给定的孤立最小点（$ x_1，\ ldots，x_k $），我们证明存在一个稳定的Euler流族，其稳定的涡度在$ k $小区域内得到支持在$ x_i $附近，