The Steady Boundary Value Problem for Charged Incompressible Fluids:
PNP/Navier Stokes Systems
By: J.W. Jerome
The initial-boundary value
problem for the Poisson-Nernst-Planck/Navier-Stokes model was
investigated in [Nonlinear Analysis 71 (2009), e2487--e2497],
where an existence theory was demonstrated,
based upon Rothe's method of horizontal lines.
In this article,
the steady case is considered,
and the existence of a weak solution
is established for the boundary-value problem.
As noted in the above-mentioned citation,
the model assumes significance because of its connection to
the electrophysiology of the cell, including
neuronal cell monitoring
and microfluidic devices in biochip technology.
The model has also been used in other applications, including
electro-osmosis. The steady model is especially important in ion channel
modeling, because the channel remains open for milliseconds, and the
transients appear to decay on the scale of tens of nanoseconds.
This article has appeared in the Journal of Nonlinear Analysis:
vol. 74 (2011), 7486--7498;
DOI: 10.1016/j.na.2011.08.003. It can be
viewed in the following format.
- Adobe PDF file