ANELASTIC APPROXIMATION OF THE GROSS-PITAEVSKII EQUATION FOR GENERAL INITIAL DATA

Abstract

We perform a rigorous analysis of the anelastic approximation for the Gross-Pitaevskii equation with x-dependent chemical potential. For general initial data and periodic boundary condition, we show that as epsilon -> 0, equivalently the Planck constant tends to zero, the density vertical bar psi(epsilon)vertical bar(2) converges toward the chemical potential rho(0)(x) and the velocity field converges to the anelastic system.