Analyticity of the inhomogeneous incompressible Navier-Stokes equations

In this paper, we obtain analyticity of the inhomogeneous Navier-Stokes equations. The main idea is to use the exponential operator eϕ(t)|D|, where ϕ(t)=δ−θ(t), δ>0 is the analyticity radius of (ρ0−1,u0), and |D| is the differential operator whose symbol is given by ‖ξ‖l1. We will show that for sufficiently small initial data, solutions are analytic globally in time in critical Besov spaces.