Analytical Approaches to Charge Transport in a Moving Medium

By: Joseph W. Jerome

We consider electrodiffusion in an incompressible electrolyte medium which is in motion. The Cauchy problem is governed by a coupled Navier-Stokes/Poisson-Nernst-Planck system. We prove the existence of a unique smooth local solution for smooth initial data, with nonnegativity preserved for the ion concentrations. We make use of semigroup ideas, originally introduced by T.~Kato in the 1970s for quasi-linear hyperbolic systems. The time interval is invariant under the inviscid limit to the Euler/Poisson-Nernst-Planck system.
This paper will appear in Transport Theory and Statistical Physics 31 (2002), pp. 333--366. It can be viewed in the following format: