Nernst–Planck–Navier–Stokes Systems far from Equilibrium

Peter Constantin, Mihaela Ignatova, Fizay Noah Lee

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We consider ionic electrodiffusion in fluids, described by the Nernst–Planck–Navier–Stokes system. We prove that the system has global smooth solutions for arbitrary smooth data in bounded domains with a smooth boundary in three space dimensions, in the following situations. We consider: a arbitrary positive Dirichlet boundary conditions for the ionic concentrations, arbitrary Dirichlet boundary conditions for the potential, arbitrary positive initial concentrations, and arbitrary regular divergence-free initial velocities. Global regularity holds for any positive, possibly different diffusivities of the ions, in the case of two ionic species, coupled to Stokes equations for the fluid. The result also holds in the case of Navier–Stokes coupling, if the velocity is regular. The same global smoothness of solutions is proved to hold for arbitrarily many ionic species as well, but in that case we require all their diffusivities to be the same.

Original languageEnglish (US)
Pages (from-to)1147-1168
Number of pages22
JournalArchive for Rational Mechanics and Analysis
Issue number2
StatePublished - May 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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