Global Well-posedness Of The Strong Solutions Of The Initial Boundary Value Problems For Two Kinds Of Micropolar Fluid Equations

In this paper,we mainly study the global well-posedness of the strong solutions of the initial boundary value problems for two kinds of micropolar fluid equations.In the first part of this paper,we prove the global well-posedness and asymptotic stability of the strong solution of the initial boundary value problem of micropolar fluid equations with a damping term in a bounded domain ?(?)R3.Precisely,for the given initial value u0?V?L?+1(?),?0?H1,the external force function f,g?Lloc2(R+;L2(?)),the damping index ??3 and ?(v+k)>1,in Chapter 3,we prove the global existence and uniqueness of the strong solution with large initial values for the equations(1.1.1),and that the strong solution converges exponentially to a non-zero steady state solution in the sense of L2 norm.In the second part of this paper,we consider the global well-posedness of the strong solution of the initial boundary value problem of magnetic micropolar fluid equations without magnetic diffusion and thermal diffusion term in a bounded domain ?(?)R2.When the initial values satisfy u0,?0?H01?H2,b0?H2,?0?H1,in Chapter 4,we prove the existence and uniqueness of the global strong solutions of the equations(1.1.2)by using Bootstrap argument.