加性退化噪声下准地转流方程的指数遍历性

Exponential Ergodicity of Quasi-Geostrophic Flows Equations with Additive Noise

考虑了有界区域上带退化加性噪声的随机准地转流方程.这是一类关于大尺度地转物理流的经典数学模型,被广泛运用在气象学、海洋大气科学和地球物理流体力学中.退化噪声使得该随机系统的研究变得更加困难,通过构建一个新函数和运用遍历理论,最终获得了该准地转流方程的指数遍历性.

Examined here in this paper are the stochastic quasi-geostrophic flows equations with additive degenerate noise on a bounded domain, which is a classical kind of mathematical model concerning large-scale Geostrophic flow, and is widely used in meteorology, marine atmospheric science and geophysical fluid mechanics. The degenerate noise makes the stochastic system even harder to tackle. By constructing a new function and applying the theory of ergodicity,the exponential ergodicity of stochastic quasi-geostrophic flows equations is thus obtained.