Equivalence between invariant measures and statistical solutions for the 2D non-autonomous magneto-micropolar fluid equations

In this article, we aim to investigate the regularity of the statistical solution for a 2D non-autonomous magneto-micropolar fluid system as well as the relationship between invariant measure and statistical solution. First, in order to get the regularity of the statistical solution, we prove the existence and regularity of pullback attractor for the system. Then we obtain that the statistical solution possesses some regularity properties by using the regularity of pullback attractor. Finally, we show that the statistical solution is actually an invariant measure for the system under consideration.

Automated summary

This article investigates the regularity of the statistical solution for a 2D non-autonomous magneto-micropolar fluid system, as well as the relationship between invariant measure and statistical solution. The existence and regularity of pullback attractor for the system is proved to determine the regularity of the statistical solution, which is shown to be an invariant measure for the system under consideration.