Semiclassical Limit of Nonlinear Schrodinger Equation (II)

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.