Charged Fluids in Porous Media

Abstract

The Nernst-Planck-Darcy system models ionic electrodiffusion in porous media. We consider the system for two ionic species with opposite valences. We prove that the initial value problem for the Nernst-Planck-Darcy system in periodic domains in two or three dimensions has global weak solutions in $W^{1,p}$ ($p\ge 2$). We obtain furthermore global existence and uniqueness of smooth solutions for arbitrary large data.

arXiv admin note: text overlap with arXiv:2101.03199

References in corpus (2)

• Existence, Uniqueness, Regularity and Long-term Behavior for Dissipative Systems Modeling Electrohydrodynamics
• Nernst-Planck-Navier-Stokes systems near equilibrium