Exact solutions of two dimensional Euler equations for incompressible fluid flows are found by the functional separation of variables. More specifically, two independent variables are considered in the Cartesian coordinates, polar coordinates and also general orthogonal curvilinear coordinates which include elliptic, parabolic and hyperbolic systems. Several new solutions are obtained and other classical solutions are rediscovered.

中文翻译：

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二维稳态欧拉方程的泛函分离精确解

不可压缩流体流动的二维欧拉方程的精确解是通过变量的函数分离找到的。更具体地，在笛卡尔坐标、极坐标以及包括椭圆、抛物线和双曲系统的一般正交曲线坐标中考虑两个自变量。获得了一些新的解决方案，并重新发现了其他经典解决方案。