Anelastic Approximation of the GrossPitaevskii equation for General Initial Data
Abstract
We perform a rigorous analysis of the anelastic approximation for the GrossPitaevskii equation with $x$dependent chemical potential. For general initial data and periodic boundary condition, we show that as $\eps\to 0$, equivalently the Planck constant tends to zero, the density $\psi^{\eps}^{2}$ converges toward the chemical potential $\rho_{0}(x)$ and the velocity field converges to the anelastic system. When the chemical potential is a constant, the anelastic system will reduce to the incompressible Euler equations. The resonant effects the singular limit process and it can be overcome because of oscillationcancelation.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.00310
 Bibcode:
 2015arXiv151200310L
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics