Statistical solution and partial degenerate regularity for the 2D non-autonomous magneto-micropolar fluids

Abstract

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.