Global existence and long term behavior of 2d electro-hydrodynamics

We study the equations of a two dimensional incompressible Newtonian fluid coupled with a dispersive parabolic-elliptic system on bounded domains. Global in time weak solutions are shown to exist and converge with a rate to the stationary solution for L^2 initial data. This paper extends and improves on a body of work surrounding the Debye-Huckel system to the hydrodyanamical case.