Name
Title | ||
|---|---|---|
A Generalized Poisson-Nernst-Planck-Navier-Stokes Model on the Fluid with the Crowded Charged Particles: Derivation and Its Well-Posedness. |
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-NavierStokes 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. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/16M1055104 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
Poisson-Nernst-Planck-Navier-Stokes equations,energetic variational approach,well-posedness,cross-diffusion | Compressibility,Mathematical optimization,Mathematical analysis,Matrix (mathematics),Diagonally dominant matrix,Planck,Classical mechanics,Charged particle,Thermodynamic equilibrium,Physics,Nernst equation,Stability theory | Journal |
Volume | Issue | ISSN |
48 | 5 | 0036-1410 |
Citations | PageRank | References |
1 | 0.43 | 0 |
Authors | ||
3 | ||