论文标题
压缩准晶格方程的平衡统计力学
Equilibrium Statistical Mechanics of Barotropic Quasi-Geostrophic Equations
论文作者
论文摘要
我们考虑描述在通道中具有地形效应和β平面近似Coriolis力的频率的方程式，其中大规模的平均流量与较小的尺度相互作用。与第一积分能量和肠相关的吉布斯措施是由分布空间支持的高斯措施。我们为压缩方程定义了合适的弱配方，并证明存在固定溶液保存吉布斯措施，从而为模型的平衡统计力学提供了严格的无限二维框架。
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 stationary solution preserving Gibbsian measures, thus providing a rigorous infinite-dimensional framework for the equilibrium statistical mechanics of the model.
