Semiclassical Limit of Nonlinear Schrodinger Equation (II)

Abstract

" In this paper, we use the Wigner measure approach to study the semiclassical limit of nonlinear Schrödinger equation in small time. We prove that: the limits of the quantum density: ρ^∈ =: |ψ^∈|² and the quantum momentum: J^∈ =: ∈Im(\\overline{ψ^∈}∇ψ^∈) satisfy the compressible Euler equations before the formation of singularities in the limit system."