Global existence and temporal decay of large solutions for the Poisson–Nernst–Planck equations in low regularity spaces

Abstract

We are concerned with the global existence and decay rates of large solutions for the Poisson-Nernst-Planck equations. Based on careful observation of algebraic structure of the equations and using the weighted Chemin-Lerner-type norm, we obtain the global existence and optimal decay rates of large solutions without requiring the summation of initial densities of a negatively and positively charged species that is small enough. Moreover, the large solution is obtained for initial densities belonging to the low regularity Besov spaces with different regularity and integral indices, which indicates more specific coupling relations between the difference and the summation of negatively and positively charged densities.

Global Existence of Large Solutions for the 3D incompressible Navier--Stokes--Poisson-- Nernst--Planck Equations

“…In this subsection, we recall the following bilinear estimates which are crucial steps to the proof of Theorem 1.1, for the detailed proofs of these bilinear estimates, we refer the readers to see [30][31][32]. Here and in the sequel we denote (d j ) j∈Z a generic element of l 1 (Z) such that d j ≥ 0 and j∈Z d j = 1.…”