Statistical Solution And Its Degenerate Regularity For Two Kinds Of Fluid Equations

Statistical solution is very important in the study of fluid dynamics.The main contents of this master thesis are concerned with the equations of the 3D autonomous incompressible Navier-Stokes and 3D autonomous incompressible magneto-micropolar fluid on their statistical solutions and its degenerate regularity.Firstly,the thesis proves,for the 3D autonomous incompressible Navier-Stokes equations,if the external force belongs to H-1 and the generalized 3D Grashof number is less than 2.057,then its weak trajectory statistical solution possesses partial degenerate regularity;if the external force belongs to L2 and the generalized 3D Grashof number is less than 2.057,then its weak trajectory statistical solution is regular.Secondly,this thesis also investigates the existence and degenerate regularity of the projected statistical solutions for the 3D autonomous incompressible magneto-micropolar fluid equations and proves the projected statistical solution possesses(partial)degenerate regularity provided that the generalized Grashof number is small enough.