A generalized Poisson-Nernst-Planck-Navier-Stokes model on the fluid with the crowded charged particles: Derivation and its well-posedness

Yong Wang, Chun Liu, Zhong Tan

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We derive a hydrodynamic model of the compressible conductive fluid by using an energetic variational approach, which could be called a generalized Poisson-Nernst-Planck-Navier-Stokes system. This system characterizes the micro-macro interactions of the charged fluid and the mutual friction between the crowded charged particles. In particular, it reveals the cross-diffusion phenomenon which does not happen in the fluid with the dilute charged particles. The cross-diffusion is tricky; however, we develop a general method to show that the system is globally asymptotically stable under small perturbations around a constant equilibrium state. Under some conditions, we also obtain the optimal decay rates of the solution and its derivatives of any order. Our method will apply equally well to a class of cross-diffusion systems if their linearized diffusion matrices are diagonally dominant.

Original languageEnglish (US)
Pages (from-to)3191-3235
Number of pages45
JournalSIAM Journal on Mathematical Analysis
Volume48
Issue number5
DOIs
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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