Conservation laws, together with the Gauss law for electrostatics, have been used to model charge transport in solid state semiconductors and in electrolytes for several decades. The determination of the current density is an important aspect of the modeling. In applications to ion channels, and to electrodiffusion more generally, there has been recent interest in the effects of the ambient fluid on current density. We discuss the mathematical model for this case: the Poisson-Nernst-Planck/Navier-Stokes model. The Cauchy problem was investigated by the speaker in [Transport Theory Statist. Phys. 31 (2002), 333--366], where a local existence-uniqueness theory was demonstrated, based upon Kato's framework for evolution equations. In this talk, the proof of existence of a global distribution solution for the model is discussed, in the case of the initial-boundary value problem. Connection of the above analysis to significant applications is also discussed.