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.