The Nernst-Planck-Navier-Stokes (NPNS) system models electrodiffusion of ions in a fluid. After a brief overview of the state of the art of the relevant global regularity theory, we discuss the long time behavior of solutions. In the case of equilibrium boundary conditions, solutions converge to unique steady states, which approximately satisfy pointwise electroneutrality in the interior, away from the boundaries. In the case of nonequilibrium boundary conditions, characterized by general Dirichlet boundary conditions for the ionic concentrations, we show that electroneutrality continues to hold in a space-time averaged sense, for large times. Time permitting, we also discuss the existence of a finite dimensional global attractor for the solution map to the NPNS system. The topics discussed include joint work with Peter Constantin and Mihaela Ignatova.

https://arizona.zoom.us/j/82763762677