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- Mathematics; Inhomogeneous Navier– Stokes equations; Critical spaces; Gevrey estimates
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.