We consider equations describing a barotropic inviscid flow in a channel with topography effects and beta-plane approximation of Coriolis force, in which a large-scale mean flow interacts with smaller scales. Gibbsian measures associated to the first integrals energy and enstrophy are Gaussian measures supported by distributional spaces. We define a suitable weak formulation for barotropic equations, and prove existence of a solution preserving Gibbsian measures, thus providing a rigorous infinite-dimensional framework for the equilibrium statistical mechanics of the model.

中文翻译：

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正压准地转方程的平衡统计力学

我们考虑描述具有地形效应和科里奥利力的β平面近似的通道中的正压无粘性流动的方程，其中大尺度平均流动与较小尺度相互作用。与第一积分能量和熵相关的吉布斯测度是分布空间支持的高斯测度。我们为正压方程定义了一个合适的弱公式，并证明了一个保留吉布斯测度的解的存在，从而为模型的平衡统计力学提供了一个严格的无限维框架。