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).
Guo et al. (2026) studied this question.