Stability of the nonconstant stationary solution to the damped Poisson–Nernst–Planck–Euler equations

Abstract

We study the stability of the stationary solution to the three‐dimensional damped Poisson–Nernst–Planck–Euler equations. We show that the stationary system has and only has a semitrivial solution under a general nonconstant doping profile. Under small initial data, we prove the existence and uniqueness of the global strong solution to the nonstationary system. We also obtain the optimal convergence rate of the norm of the solution toward the semitrivial stationary solution as time tends to infinity.