论文标题
与退化随机强迫的分数磁性流动力方程的指数混合
Exponential mixing for the fractional Magneto-Hydrodynamic equations with degenerate stochastic forcing
论文作者
论文摘要
我们确定了仅在磁方程中起作用的变性随机强迫的MHD方程的不变度度量的存在，唯一性和指数吸引力。核心挑战是建立与该系统相对应的相关的马尔可夫半群的时间渐近平滑特性。为了实现这一目标，我们充分利用了对流结构的特征，以发现一种新型的Hörmander型条件，该条件仅允许在磁性方向上发出几个声音。
We establish the existence, uniqueness and exponential attraction properties of an invariant measure for the MHD equations with degenerate stochastic forcing acting only in the magnetic equation. The central challenge is to establish time asymptotic smoothing properties of the associated Markovian semigroup corresponding to this system. Towards this aim we take full advantage of the characteristics of the advective structure to discover a novel Hörmander-type condition which only allows for several noises in the magnetic direction.
