Random attractors for the stochastic Nernst–Planck–Navier–Stokes system with multiplicative white noise

In this paper, we consider the 2D periodic stochastic Nernst–Planck–Navier–Stokes equations with body forces perturbed by multiplicative white noise. We first transform the stochastic Nernst–Planck–Navier–Stokes system into the deterministic system and address the problem of global well-posedness of the solution. Then, we generate a corresponding random dynamical system and dedicate to proving the existence of a compact random attractor for such random dynamical system. Furthermore, upper semicontinuity of the random attractor is established when the noise intensity approaches zero.