Global Well-posedness Of Strong Solutions To The Two Kinds Of Micropolar Fluid Equations

In this paper,we study the global well-posedness of strong solutions to the two kinds of micropolar fluid equations.The first problem is to consider the global well-posedness of the strong solutions of the magnetic micropolar fluid equations.To be precise,if the initial value of(u0,ω0,b0)∈H1(R3)is not subject to any small restrictions,we can prove the local existence and uniqueness of the strong solutions of the equations(1.1.1);If the initial value ‖(u0,ω0,b0)‖L22(‖▽u0‖L22+‖▽ω0‖L22+‖▽b0‖L22+‖▽ × u0-2ω0‖L22),is reasonably small,we can prove the global well-posedness of strong solutions of the equations(1.1.1),by means of energy estimation and the classical continuity method.The second problem is to consider the global well-posedness of strong solutions for the system of micropolar fluid equations with damping and heat conduction effect,that is,if the initial value satisfies(u0,ω0,θ0)∈ H2(R3)×H2(R3)×H1(R3)∩W1,3(R3),the nonlinear index α>1,we can prove the global existence and uniqueness of strong solutions of the equations(1.1.2).