Asymptotic Behavior Of Solutions For Two Two-Dimensional Non-Newtonian Fluid

Fluicd mechanics is applied widely in physics, biology, atmospheric,oceanic science and aerospace industry and other fields. Non-Newtonian fluid mechanics is an important branch of modern fluid mechanics.This master thesis mainly studies the asymptotic behavior of solu-tions for two two-dimensional incompressible non-Newtonian fluid. First of all, the paper introduces the number estimation of determining modes and determining nodes to the two non-Newtonian flow equations. The number of finite determining modes indicates that the asymptotic be-havior of solutions to the two equations is completely determined by the asymptotic behavior of their front limited fourier modes, and the number of finite determining nodes demonstrates that, the asymptotic behavior of solutions to the two equations is completely determined by the asymptotic behavior of their solutions in the finite points. Then, we prove the existence of the pullback attractor and invariant measure of the Ladyzhenskaya fluid model.It will be useful for studying the asymptotic behavior of solutions for non-Newtonian fluid. Because of the limited property of determining modes and determining nodes, it provides a theoretical basis for the numerical simulation.