Quasineutral Limit of the Schrodinger-Poisson System in Coulomb Gauge

Abstract

The zero Debye length asymptotic of the Schrodinger-Poisson system in Coulomb gauge for ill-prepared initial data is studied. We prove that when the scaled Debye length lambda -> 0, the current density defined by the solution of the Schrodinger-Poisson system in the Coulomb gauge converges to the solution of the rotating incompressible Euler equation plus a fast singular oscillating gradient vector field.