In this article, the authors investigate the non-autonomous magneto-micropolar fluids in a two-dimensional bounded domain. They first prove the existence of a pullback attractor for the associated process. Then, they construct a family of invariant Borel probability measures supported on the pullback attractor and prove that this family of probability measures is indeed a statistical solution for the magneto-micropolar fluids. Further, they establish that if some form of the Grashof number is small enough, then the pullback attractor degenerates to a single bounded complete trajectory, which implies the partial degenerate regularity of the statistical solution in the sense that it is supported on a set in which the weak solutions are in fact partially strong solutions.

在本文中，作者研究了二维有界域中的非自主磁微极性流体。他们首先证明了相关过程存在回撤吸引子。然后，他们构造了支持在回拉吸引子上的不变Borel概率测度族，并证明了这种概率测度族确实是磁微极性流体的统计解决方案。此外，他们确定，如果某种形式的Grashof数足够小，则回撤吸引子会退化为单个有界的完整轨迹，这意味着统计解的部分退化正则性在某种意义上得到了支持。弱解决方案实际上是部分强解决方案。