复杂地形情况下大气动态模型的弱解和吸引子的存在性

The Existence of Weak Solutions and the Trajectory Attractors to the Model of Climate Dynamics

该文研究了一个适合应用于天气预报的大气模型,模型考虑到地形对大气的动力强迫作用,保留了大气气流的辐散效应.首先采用了适当的函数空间,引入了合理的算子表达形式,将复杂的大气动态方程组用一个简单的抽象的算子方程表示,由此给出了模型弱解的定义.然后利用Galerkin方法证明了弱解的存在性.通过构造大气动态方程组轨道吸引集证明相应的轨道吸引子的存在性.

In this paper, the model of climate for weather forecast is studied, in which the pressing force of topography on atmosphere and the divergent effect of airflow are included. The suitable space of functions and the reasonable operators are selected to represent the complex atmosphere dynamical equations by the simple abstract operator equation, such that the weak solution can be defined. Then the existence of the weak solution is proved by Galerkin method, and the asymptotic behaviors of the weak solution is described by the trajectory attractors.