In this paper, we prove the global existence and uniqueness of solution to
d-dimensional (for d=2,3) incompressible inhomogeneous Navier-Stokes
equations with initial density being bounded from above and below by some
positive constants, and with initial velocity u0​∈Hs(R2) for s>0 in
2-D, or u0​∈H1(R3) satisfying |u_0|_{L^2}|\na u_0|_{L^2} being
sufficiently small in 3-D. This in particular improves the most recent
well-posedness result in [10], which requires the initial velocity u0​∈H2(Rd) for the local well-posedness result, and a smallness condition on
the fluctuation of the initial density for the global well-posedness result