Global solutions of two-dimensional inhomogeneous incompressible micropolar fluids with bounded density

The micropolar fluids constitute a substantial generalization of the Navier-Stokes equations, and open a new field of the potential application of the complex fluids. In this paper, considering two-dimensional (2D) inhomogeneous incompressible micropolar fluids, we obtain the global existence of solution if the initial data satisfy (u0,w0)∈L2(R2)∩Ḃp,1−1+2/p(R2),1−ρ0−1(R2)∈Ḃλ,22/λ(R2)∩L∞(R2), p∈[2,∞),λ∈1,∞,1/2<1/p+1/λ≤1. The main innovation of this paper is to establish some higher order time weighted regularity estimates of the solution, which allows us to get the uniqueness of solution without any additional assumptions on the initial density. In particular, this strategy can also be applied to prove the uniqueness of solution of 2D inhomogeneous incompressible Navier-Stokes system, and hence gives improvement of some recent corresponding results.