Global well-posedness for the Navier-Stokes-Nernst-Planck-Poisson system in dimension two

In this paper, we first prove the global existence for the Cauchy problem of the Navier-Stokes-Nernst-Planck-Poisson (NSNPP) system in dimension two. Then we establish the L2 decay estimates of the solutions by using the Fourier splitting method.