A GENERALIZED POISSON-NERNST-PLANCK-NAVIER-STOKES MODEL ON THE FLUID WITH THE CROWDED CHARGED PARTICLES: DERIVATION AND ITS WELL-POSEDNESS

作者：Wang, Yong; Liu, Chun; Tan, Zhong^*

来源：SIAM Journal on Mathematical Analysis, 2016, 48(5): 3191-3235.

DOI：10.1137/16M1055104

• Poisson-Nernst-Planck-Navier-Stokes equations
• energetic variational approach
• well-posedness
• cross-diffusion

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.

• 出版日期2016
• 单位厦门大学