On the Motion of Viscous Fluids in the Presence of Diffusion

Source abstract

We consider the motion of a viscous incompressible fluid consisting of two components with a diffusion effect obeying Fick’s law. We prove: (i) the existence for two-dimensional flows of a (unique) global solution if the diffusion coefficient $\lambda$ is small; (ii) the convergence (as $\lambda \to 0$) for two- and three-dimensional motions towards the corresponding solutions of the Navier–Stokes system for nonhomogeneous fluids.