
handle: 20.500.11824/1387 , 11104/0314773 , 11571/1364694
In this article we study a system of nonlinear PDEs modelling the electrokinetics of a nematic electrolyte material consisting of various ions species contained in a nematic liquid crystal. The evolution is described by a system coupling a Nernst-Planck system for the ions concentrations with a Maxwell's equation of electrostatics governing the evolution of the electrostatic potential, a Navier-Stokes equation for the velocityfield, and a non-smooth Allen-Cahn type equation for the nematic directorfield. We focus on the two-species case and prove apriori estimates that provide a weak sequential stability result, the main step towards proving the existence of weak solutions.
Compactness, A-priori estimates, Navier-Stokes equations for incompressible viscous fluids, Weak-sequential stability, a-priori estimates, weak-sequential stability, Nernst-planck equation, 530, A priori estimates in context of PDEs, 510, Navier-Stokes system, Navier-stokes system, Nernst-Planck equation, compactness, PDEs in connection with optics and electromagnetic theory
Compactness, A-priori estimates, Navier-Stokes equations for incompressible viscous fluids, Weak-sequential stability, a-priori estimates, weak-sequential stability, Nernst-planck equation, 530, A priori estimates in context of PDEs, 510, Navier-Stokes system, Navier-stokes system, Nernst-Planck equation, compactness, PDEs in connection with optics and electromagnetic theory
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