##
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: