A generalized Poisson-Nernst-Planck-Navier-Stokes model on the fluid with the crowded charged particles: derivation and its well-posedness (Q2821656)

In this article, the authors study a generalized Poisson-Nernst-Planck-Navier-Stokes system which characterizes the micro-macro interactions of the charged fluid and the mutual friction between the crowded charged particles. The main theorem gives an existence result in the class of Sobolev spaces. If the initial data is small in the Sobolev space $H^3$, then global existence and uniqueness are obtained. \par With additional information on the initial data stated in terms of Besov spaces, some decay of the solutions are given.