Global well-posedness for the incompressible Navier–Stokes equations with density-dependent viscosity coefficient

This paper is concerned with an initial–boundary value problem of the incompressible Navier–Stokes equations with density-dependent viscosity in a smooth bounded domain Ω⊂R3Ω⊂R3. The global well-posedness of strong solutions with large oscillations is established in both non-vacuum and vacuum cases, provided the initial velocity is suitably small in certain sense. It is worth pointing out that there isn't any smallness condition on the density and its gradient.