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On uniqueness results for an elliptic‐parabolic‐system of partial differential equations arising in dynamic electrowetting
Author(s) -
Fontelos M.A.,
Grün G.
Publication year - 2013
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200200
Subject(s) - electrowetting , uniqueness , partial differential equation , electric field , mathematical analysis , poisson's equation , electrokinetic phenomena , differential equation , mathematics , uniqueness theorem for poisson's equation , field (mathematics) , physics , classical mechanics , materials science , voltage , quantum mechanics , pure mathematics , nanotechnology
Abstract We 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)).