Local well-posedness to the free boundary problem of incompressible Euler-Poisson-Nernst-Planck system

Abstract

We are concerned with the local well-posedness of three-dimensional incompressible charged fluids bounded by a free-surface. We show that the Euler-Poisson-Nernst-Planck system, wherein the pressure and electrostatic potential vanish along the free boundary, admits the existence of unique strong (in Sobolev spaces) solution in a short time interval. Our proof is founded on a nonlinear approximation system, chosen to preserve the geometric structure, with the aid of tangentially smoothing and Alinhac good unknowns in terms of boundary regularity, our priori estimates do not suffer from the derivative loss phenomenon.