Abstract
We consider the Nernst-Planck-Navier-Stokes system describing the electrodiffusion of ions in a viscous Newtonian fluid. We prove the exponential nonlinear stability of constant steady states in the case of periodic boundary conditions in any dimension of space without constraints on the number of species, valences and diffusivities. We consider also the case of two spatial dimensions, and we prove the exponential stability from arbitrary large data.
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