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In this paper, we consider the 2D stochastic Nernst-Planck-Navier-Stokesequations with transport noise. By assuming the ionic species have the samediffusivity and opposite valences, we prove the global well-posedness of thesystem. Furthermore, we illustrate the enhanced dissipation phenomenon in thesystem with specific transportation noise by establishing that it enables anarbitrarily large exponential convergence rate of the solutions.

Global well-posedness and enhanced dissipation for the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise