Non-homogeneous Navier-Stokes systems with order-parameter-dependent stresses

We consider the Navier-Stokes system with variable density and variable viscosity coupled to a transport equation for an order-parameter c. Moreover, an extra stress depending on c and del c, which describes surface tension like effects, is included in the Navier-Stokes system. Such a system arises, e.g. for certain models of granular flows and as a diffuse interface model for a two-phase flow of viscous incompressible fluids. The so-called density-dependent Navier-Stokes system is also a special case of our system. We prove short-time existence of strong solution in L(q)-Sobolev spaces with q>d. We consider the case of a bounded domain and an asymptotically flat layer with a combination of a Dirichlet boundary condition and a free surface boundary condition. The result is based on a maximal regularity result for the linearized system. Copyright (C) 2010 John Wiley & Sons, Ltd.