Semiclassical Limit of Nonlinear Schrodinger Equation (II)

Abstract

" In this paper, we use the Wigner measure approach to study the semiclassical limit of nonlinear Schr\u00f6dinger equation in small time. We prove that: the limits of the quantum density: \u03c1^\u2208 =: |\u03c8^\u2208|\u00b2 and the quantum momentum: J^\u2208 =: \u2208Im(\\overline{\u03c8^\u2208}\u2207\u03c8^\u2208) satisfy the compressible Euler equations before the formation of singularities in the limit system."