In two space dimensions and under the assumptions that the initial density rho(0) has a positive lower bound and the initial data rho(0) - rho(infinity), u(0) is an element of H-s(R-2) for s > 2, we prove the global existence and uniqueness of smooth solutions to a model of the inhomogeneous Navier-Stokes equations with the viscous coefficient depending on the density of the fluid.
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