Global Weak Solutions for an Incompressible Charged Fluid with
Multi-Scale Couplings:
Initial-Boundary Value Problem
By: Joseph W. Jerome and Riccardo Sacco
The Cauchy problem for the Poisson-Nernst-Planck/Navier-Stokes model was
investigated by the first author in
[Transport Theory Statist. Phys. 31 (2002), 333--366],
where a local existence-uniqueness theory was demonstrated,
based upon Kato's framework for examining evolution equations.
In this article, the existence of a global weak solution
is proved to hold for the model, in the case of
the initial-boundary value problem.
Connection of the above analysis to significant
applications is addressed, including bio-hybrid devices in
neuronal cell monitoring, bio-reactor devices in tissue
engineering and microfluidic devices in Lab-On-Chip technology.
This paper has been presented at WCNA-5, held in
Orlando in July, 2008, and
has appeared electronically in Nonlinear Analysis: vol. 71 (2009), pp.
e2487--e2497.
doi:10.1016/j.na.2009.05.047