Global Well-posedness Of Solutions To The Incompressible Micropolar Equations With Partial Viscosity

In this paper,we mainly study the well-posedness of strong solutions to the incompressible micropolar equations with partial viscosity in R3.Firstly,we consider the local well-posedness of the strong solution with large initial data and prove the global well-posedness of the strong solution under the condition of small initial data to the incompressible micropolar equations with partial viscosity.More precisely,when the initial velocity field u0 ∈H2(R3)and angular velocity field ω0 ∈H2(R3),we prove the local existence and uniqueness of the strong solution by the classical viscosity vanishing method;when the initial data E0=:(‖u0‖L22+‖ω0‖L22)(‖▽u0‖L22+‖▽ω‖L22)is sufficiently small,we prove the global existence of the strong solution in this paper.On the basis of the results of the first part,taking account of the effect of the damping term,we prove the global well-posedness of the strong solution with large initial data to the incompressible micropolar equations with partial viscosity in the second part of this paper,that is,when the damping index α≥3/2,we prove the global well-posedness of the strong solution with large initial data.The conclusion shows that the damping term plays a positive role in the stability of the solution.