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Existence theory for a Poisson-Nernst-Planck model of electrophoresis

By Luciano Bedin and Mark Thompson


A system modeling the electrophoretic motion of a charged rigid macromolecule immersed in a incompressible ionized fluid is considered. The ionic concentration is governing by the Nernst-Planck equation coupled with the Poisson equation for the electrostatic potential, Navier-Stokes and Newtonian equations for the fluid and the macromolecule dynamics, respectively. A local in time existence result for suitable weak solutions is established, following the approach of Desjardins and Esteban [Comm. Partial Diff. Eq., 25 (2000), 1399--1414].Comment: This paper has been withdrawn by the authors due to several misprints. A corrected and full version was published in Comm. Pure Appl. Anal. 12(1), 157-206, (2013

Topics: Mathematics - Analysis of PDEs, Mathematical Physics
Year: 2014
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