Global well-posedness for 3D incompressible inhomogeneous micropolar flows

In this paper, we consider the Cauchy problem for $ 3 $-D incompressible inhomogeneous micropolar flows in $ {\mathbb R}^{3} $. The global existence and uniqueness of the strong solution to the $ 3 $-D incompressible inhomogeneous micropolar flows are established provided that the initial density data $ \|\rho_0-1\|_{L^\infty} $ is small and the initial velocity and angular velocity $ (u_{0},w_{0})\in \dot{B}_{p,1}^{-1+3/p}({\mathbb R}^3)\cap L^{\alpha}({\mathbb R}^3) $ is sufficiently small in $ \dot{B}_{p,1}^{-1+3/p}({\mathbb R}^3)(1\leq p<3) $, which extends the result of [23]. In addition, the algebraic decay estimate is also obtained.