On non-Newtonian incompressible fluids with phase transitions

A modified model for a binary fluid is analysed mathematically. The governing equations of the motion consists of a Cahn-Hilliard equation coupled with a system describing a class of non-Newtonian incompressible fluid with p-structure. The existence of weak solutions for the evolution problems is shown for the space dimension d=2 with p(greater than or equal to) 2 and for d=3 with p(greater than or equal to) 2 11/5. The existence of measure-valued solutions is obtained for d=3 in the case 2(less than or equal to) 2 p< 11/5. Similar existence results are obtained for the case of nondifferentiable free energy, corresponding to the density constraint |(psi)| (less than or equal to)1. We also give regularity and uniqueness results for the solutions and characterize stable stationary solutions.