Global Well-posedness Of Solutions To The Incompressible Micropolar Fluid Equations

Micropolar fluid is used to represent a class of fluid with asymmetric stress tensor.Compared with the classical Navier-Stokes equations,it can describe the dynamic behavior of some special fluids,such as polymer fluid,liquid crystal,animal blood,colloidal fluid and so on.Therefore,its mathematical theory attracts a lot of attentions of the mathematicians.The main character of this paper is that the initial vacuum is allowed in the initial density.we mainly studies global well-posedness and the exponential decay of solutions of inhomogeneous incompressible micropolar fluid equations,in which the initial density allows for vacuum and discontinuity.The thesis is divided into two parts.The first part of the thesis is to consider the global well-posedness of solutions of 2D incompressible micropolar fluid equations.Specifically,we only need initial data(?0,u0,?0)?L?×H0,?1,then we can prove that it admits a global,unique solution with a large initial value with regularity as low as possible.The second part of the thesis is to consider the global well-posedness of solutions of 3D incompressible micropolar fluid equations.Specifically,in the 3D case,we assume that the initial data(?0,u0,?0)?L?×H0,?1 × H01,if there is a(small)positive constant? such that (?)then there exists a unique global solution to the 3D inhomogeneous incompressible micropolar fluid equations.As a byproduct,the exponential decay in time of the solution is also established by virtue of the a priori time-weighted estimates.