Abstract In this article, we first prove, from the viewpoint of infinite dynamical system, sufficient conditions ensuring the existence of trajectory statistical solutions for autonomous evolution equations. Then we establish that the constructed trajectory statistical solutions possess invariant property and satisfy a Liouville type equation. Moreover, we reveal that the equation describing the invariant property of the trajectory statistical solutions is a particular situation of the Liouville type equation. Finally, we study the equations of three-dimensional incompressible magneto-micropolar fluids in detail and illustrate how to apply our abstract results to some concrete autonomous evolution equations.

中文翻译：

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演化方程的轨迹统计解和刘维尔型方程：抽象结果和应用

摘要 本文首先从无限动力系统的角度证明了自主演化方程轨迹统计解存在的充分条件。然后我们确定构造的轨迹统计解具有不变性并满足Liouville型方程。此外，我们揭示了描述轨迹统计解不变性的方程是Liouville型方程的一种特殊情况。最后，我们详细研究了三维不可压缩磁微极流体的方程，并说明了如何将我们的抽象结果应用于一些具体的自主演化方程。