On the Nernst-Planck-Navier-Stokes system
Peter Constantin, Mihaela Ignatova
TL;DR
This paper analyzes the mathematical properties of the Nernst-Planck-Navier-Stokes system modeling ionic electrodiffusion, proving global existence and stability results for large data in bounded two-dimensional domains.
Contribution
It provides the first rigorous proof of global existence and stability for the coupled Nernst-Planck-Navier-Stokes system with various boundary conditions.
Findings
Global existence of solutions established
Stability results proven for large data
Applicable to bounded two-dimensional domains
Abstract
We consider ionic electrodiffusion in fluids, described by the Nernst-Planck-Navier-Stokes system in bounded domains, in two dimensions, with Dirichlet boundary conditions for the Navier-Stokes and Poisson equations, and blocking (vanishing normal flux) or selective (Dirichlet) boundary conditions for the ionic concentrations. We prove global existence and stability results for large data.
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