We consider the inhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity coefficient in two space dimensions. These equations describe the motion of a fluid with variable density and viscosity, which arises for example when mixing two immiscible fluids with different densities and viscosities. In this talk we prove the propagation of regularity of density patches, even for largely varying, discontinuous viscosity coefficients. This talk is based on joint work with Xian Liao.