  We consider in this paper a numerical approximation of
Poisson-Nernst-Planck-Navier- Stokes (PNP-NS) system. We construct a decoupled
semi-discrete and fully discrete scheme that enjoys the properties of
positivity preserving, mass conserving, and unconditionally energy stability.
Then, we establish the well-posedness and regularity of the initial and
(periodic) boundary value problem of the PNP-NS system under suitable
assumptions on the initial data, and carry out a rigorous convergence analysis
for the fully discretized scheme. We also present some numerical results to
validate the positivity-preserving property and the accuracy of our scheme.
