Abstract
The Nernst-Planck-Navier-Stokes system models electrodiffusion of ions in a fluid. We prove global existence of solutions in bounded domains in three dimensions with either blocking (no-flux) or uniform selective (special Dirichlet) boundary conditions for ion concentrations. The global existence of strong solutions is established for initial conditions that are sufficiently small perturbations of steady state solutions. The solutions remain close to equilbrium in strong norms. The main two steps of the proof are (1) the decay of the sum of relative entropies (Kullback-Leibler divergences) and (2) the control of L2 norms of deviations by the sum of relative entropies.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 175-196 |
| Number of pages | 22 |
| Journal | Pure and Applied Functional Analysis |
| Volume | 7 |
| Issue number | 1 |
| State | Published - 2022 |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
- Control and Optimization
Keywords
- Lonic electrodiffusion
- Navicr-Stokcs
- Nernst-Planck
- Poisson-Boltzmann