Global Unique Solvability of Inhomogeneous Navier-Stokes Equations with Bounded Density

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 u(0) epsilon H-s(R-2) for s > 0 in 2-D, or u(0) epsilon H-1(R-3) satisfying parallel to u(0) parallel to(2)(L) parallel to del u(0) parallel to(2)(L) being sufficiently small in 3-D. This in particular improves the most recent well-posedness result in [10], which requires the initial velocity u(0) epsilon H-2(R-d) for the local well-posedness result, and a smallness condition on the fluctuation of the initial density for the global well-posedness result.