论文标题
随机两层准晶状体模型的指数型成分
Exponential ergodicity for a stochastic two-layer quasi-geostrophic model
论文作者
论文摘要
分析了用于大气和海洋动力学的随机培养基复杂度模型的奇异性能。更具体地说，研究了用于地球物理流的两层准地球化学模型，上层被加性噪声扰动。该模型在地球科学中很受欢迎，例如研究强迫随机风对海洋的影响。然而，严格的数学分析面临着一个挑战，即在研究的模型中，随机强迫仅在顶层上起作用，噪声构型在空间上退化。建立了解决方案法与不变度度量的指数收敛，这意味着相关的马尔可夫半群在Hölder连续功能的空间上存在光谱差距。该方法为适用于耗散SPDE的应用的通用耦合技术提供了一个通用框架。如果是两层准地藻模型，结果需要第二层遵守一定的被动条件。
Ergodic properties of a stochastic medium complexity model for atmosphere and ocean dynamics are analysed. More specifically, a two-layer quasi-geostrophic model for geophysical flows is studied, with the upper layer being perturbed by additive noise. This model is popular in the geosciences, for instance to study the effects of a stochastic wind forcing on the ocean. A rigorous mathematical analysis however meets with the challenge that in the model under study, the noise configuration is spatially degenerate as the stochastic forcing acts only on the top layer. Exponential convergence of solutions laws to the invariant measure is established, implying a spectral gap of the associated Markov semigroup on a space of Hölder continuous functions. The approach provides a general framework for generalised coupling techniques suitable for applications to dissipative SPDEs. In case of the two-layer quasi-geostrophic model, the results require the second layer to obey a certain passivity condition.
