Existence, degenerate regularity and limit behavior of trajectory statistical solution for the 3D incompressible micropolar fluids flows with damping term

Abstract

This article studies the existence, degenerate regularity and limit behavior of the trajectory statistical solution for a three-dimensional incompressible micropolar fluids flows with a damping term. The authors first prove the existence of the trajectory attractor and use it to construct the trajectory statistical solution. Then they establish that the trajectory statistical solution possesses partial regularity provided that the associated Grashof number is small enough. Finally, they investigate the limiting behavior of the trajectory statistical solution as the damping term vanishes.