  This work is concerned with the global existence of large solutions to the
three-dimensional dissipative fluid-dynamical model, which is a strongly
coupled nonlinear nonlocal system characterized by the incompressible
Navier--Stokes--Poisson--Nernst--Planck equations. Making full use of the
algebraic structure of the system, we obtain the global existence of solutions
without smallness assumptions imposed on the third component of the initial
velocity field and the summation of initial densities of charged species. More
precisely, we prove that there exist two positive constants $c_{0}, C_{0}$ such
that if the initial data satisfies \begin{align*}
  \big(\|u_{0}^{h}\|_{\dot{B}^{-1+\frac{3}{p}}_{p,1}}+\|N_{0}-P_{0}\|_{\dot{B}^{-2+\frac{3}{q}}_{q,1}}
  \big)
  \exp\Big\{C_{0}\big(\|u_{0}^{3}\|_{\dot{B}^{-1+\frac{3}{p}}_{p,1}}^{2}+(\|N_{0}+P_{0}\|_{\dot{B}^{-2+\frac{3}{r}}_{r,1}}+1)\exp\big\{C_{0}\|u_{0}^{3}\|_{\dot{B}^{-1+\frac{3}{p}}_{p,1}}\big\}+1\big)\Big\}
  \leq
  c_{0}, \end{align*} then the incompressible
Navier--Stokes--Poisson--Nernst--Planck equations admits a unique global
solution.
