Unique solvability for the density-dependent incompressible Navier-Stokes-Korteweg system

This article concerns the strong solutions for the incompressible fluid models of Korteweg type with a density-dependent viscosity and capillary coefficient in a bounded domain Ω⊂R3. It is proved that the initial boundary problem of the density-dependent incompressible fluid of Korteweg type admits a unique local strong solution, which allows the existence of initial vacuum provided the initial data satisfies a compatibility condition.