Stability of the nonconstant stationary solution to the Poisson–Nernst–Planck–Navier–Stokes equations. (October 2022)

• Record Type: Journal Article
• Authors: Shen, Rong; Wang, Yong
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: Poisson–Nernst–Planck–Navier–Stokes equations -- Nonconstant stationary solutions -- Stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103582
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study the three-dimensional Cauchy problem of the Poisson–Nernst–Planck–Navier–Stokes equations. We first show that the corresponding stationary system has a unique semi-trivial solution under a general doping profile. Under initial small perturbations around such the semi-trivial stationary solution and small doping profile, we obtain the unique global-in-time solution to the non-stationary system. Moreover, we prove the asymptotic convergence of the solution toward the semi-trivial stationary solution as time tends to infinity.