Pullback Asymptotic Behavior Of Nonautonomous Micropolar Fluid On Two-Dimensional Bounded Domains

Nonlinear partial differential equations (NPDE) is an important field of research in basic mathematics and applied mathematics, which has extensive connections with other branches of mathematics, and widely used in the technical fields of natural science and engineering.One of the main subject of NPDE is to reveal the well-posedness and the asymptotic behaviors of the solutions. As an important class of NPDE, micropolar fluid flow equations describe the motion of a class of Newtonian flow. So it is very important for engineers and scientists of researching dynamics and phenomena. This dissertation mainly proves the well-posedness and pullback asymptotic behaviors of solutions for a two-dimensional non-autonomous micropolar fluid flows and a two-dimensional non-autonomous micropolar fluid flows with infinite delays, respectively. It is arranged as follows.The first chapter summarizes the background of the micropolar fluid flow equations, as well as the classical result related the equations and the issues addressed in this thesis.The second chapter investigates the pullback asymptotic behav-iors of solutions for non-autonomous micropolar fluid flows on two-dimensional bounded domains. Firstly, it shows the global well-posedness of solutions for the equations. Then, it proves the existence and regular-ity of the pullback attractors. Finally, it analyzes the tempered behavior and H2-boundedness of the pullback attractors.The third chapter studies the well-posedness and the pullback asymp-totic behaviors of solutions for non-autonomous micropolar fluid flows with infinite delays on two-dimensional bounded domains. It first proves the global well-posedness of the solutions, then establishes the existence of the pullback attractors for the associated process.The fourth Chapter summaries the thesis of the paper.