Global regularity of two dimensional inhomogeneous incompressible   Navier-Stokes Equations with large data
  For two dimensional inhomogeneous Navier-Stokes of incompressible flows, with the assumption that the viscosity depends on the density but with a positive lower bound, using a partial regularity approach, in particular some enhanced decay estimates, we establish the global in time regularity for large data away from vacuum. 
Ning Jiang and Yilong Luo
math.AP