The 2D Euler equations with random initial condition has been investigates by Albeverio and Cruzeiro (Commun Math Phys 129:431–444, 1990) and other authors. Here we prove existence of solutions for the associated continuity equation in Hilbert spaces, in a quite general class with LlogL densities with respect to the enstrophy measure.

中文翻译：

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涡度测度下二维Euler方程在LlogL中的连续性方程

Albeverio和Cruzeiro（Commun Math Phys 129：431–444，1990）和其他作者已经研究了具有随机初始条件的二维Euler方程。在这里，我们证明了希尔伯特空间中相关联的连续性方程的解的存在性，这是一个关于旋涡测度的具有LlogL密度的相当普通的类。