On Hydrodynamic Models for LEO Spacecraft Charging

Abstract

This paper is devoted to hydrodynamic models intended to describe charging phenomena the spacecrafts evolving in Low Earth Orbits (LEO) are subject to. The models we are interested in couple the stationary Euler equations to the Poisson equation which defines the electric potential. Furthermore, the charging dynamics is embodied into the boundary conditions where the time derivative of the potential appears. We point out the main mathematical difficulties by restricting to a 1D caricature model for which we present rigorous existence results and numerical simulations.