Global large solutions to the Navier–Stokes–Nernst–Planck–Poisson equations in Fourier–Besov spaces

Abstract

In this paper, we mainly study the Cauchy problem of a d-dimensional Navier–Stokes–Nernst–Planck–Poisson equation in Fourier–Besov space. Based on its special structure, the assumption of local smallness of the initial data can be ignored to obtain the global well-posedness, and it is proved that the global existence of the solution can be obtained only if part of the initial data is small enough.