On the Nernst-Planck-Navier-Stokes Equations

Abstract: We review recent results concerning the NPNS system in 2D and 3D.

The main results are global stability and regularity results in 2D, strong nonlinear stability of Boltzmann states in 3D and unconditional global existence and regularity in 3D for large data for the NP-Stokes equations, and conditional on regularity of velocity for NPNS, in the

specific case of two ionic species with arbitrary diffusivities and the case of N ionic species with equal diffusivities. We obtain interior electroneutrality in the limit of vanishing Debye length in the stable cases.

This is joint work with M. Ignatova and F-N. Lee.

analysis of PDEs

Audience: researchers in the topic

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