Hydrodynamic limit of the Maxwell-Schrödinger equations to the compressible Euler-Maxwell equations

Abstract

We present the hydrodynamic limit of the nonlinear Maxwell-Schrödinger equations. Under the a priori boundedness assumption on the density, we show that the Maxwell-Schrödinger system converges to the compressible Euler-Maxwell system as the Planck constant tends to 0. Our analysis is based on the modulated energy estimate.