Statistical solutions and degenerate regularity for the micropolar fluid with generalized Newton constitutive law

Abstract

This paper studies the nonautonomous micropolar fluid with generalized Newton constitutive law in two‐dimensional bounded domains. We first establish that the generated continuous process of the solutions operator possesses a pullback attractor. Then we verify the existence of statistical solutions by constructing the invariant Borel probability measures. Further, we prove that the statistical solutions possess the degenerated regularity of Lusin's type provided that the Grashof number associated to the external forces is small enough.