Regularity criteria for a mathematical model for the deformation of electrolyte droplets

We prove some regularity criteria for the strong solutions to a mathematical model for the deformation of electrolyte droplets introduced by Ryham, Liu, and Zikatanov [R. J. Ryham, C. Liu, L. Zikatanov, Mathematical models for the deformation of electrolyte droplets, Discrete Contin. Dyn. Syst. Ser. B 8 (2007) 649–661]. This model is a strongly coupled system which contains the incompressible Navier–Stokes equations, the Poisson–Nernst–Planck equations and the Allen–Cahn equation, and finds many promising applications in microfluidics and materials science engineering.