M.A. Fontelos and G. Grün
The authors prove regularity results and, as a consequence, uniqueness for a system of partial differential equations arising in the study of dynamic electrowetting phenomena and more general electrokinetic processes in three space dimensions. The system consists of Stokes equations coupled with equations for the motion of electric charges, Poisson equation for computing the electric field generated by such charges and a Cahn-Hilliard equation for a phase field describing two fluids with different material parameters. The deduction and existence of weak solutions for this system was established in an earlier paper (Christof Eck et al., On a phase-field model for electrowetting, Interfaces Free Bound. 11(2),259–290, (2009)).