Existence and stability of nonequilibrium steady states of Nernst–Planck–Navier–Stokes systems

Peter Constantin, Mihaela Ignatova, Fizay Noah Lee

Research output: Contribution to journalReview articlepeer-review

3 Scopus citations


We consider the Nernst–Planck–Navier–Stokes system in a bounded domain of Rd, d=2,3 with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. We prove the existence of smooth steady state solutions and present a sufficient condition in terms of only the boundary data that guarantees that these solutions have nonzero fluid velocity. We show that all time dependent solutions of the Nernst–Planck–Stokes system in three spatial dimensions, after a finite transient time, become bounded uniformly, independently of their initial size. In addition, we consider one dimensional steady states with steady nonzero currents and show that they are globally nonlinearly stable as solutions in a three dimensional periodic strip, if the currents are sufficiently weak.

Original languageEnglish (US)
Article number133536
JournalPhysica D: Nonlinear Phenomena
StatePublished - Dec 15 2022

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


  • Electroconvection
  • Ionic electrodiffusion
  • Navier–Stokes
  • Nernst–Planck
  • Poisson–Boltzmann


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