Global solution and analyticity for incompressible Navier–Stokes equations in critical Besov–Morrey spaces

In this paper, we establish global existence, uniqueness, and spatial analyticity for solutions to the 3D inhomogeneous incompressible Navier–Stokes equations with small initial data in the critical scaling-invariant Besov–Morrey spaces. By reformulating the system via the density transformation ρ = 1 − D−1, we derive apriori estimates in Na,μ,1r-type spaces and employ Gevrey-class techniques to control the analyticity radius ψ(t).