# Anelastic Approximation of the Gross-Pitaevskii equation for General Initial Data

@article{Lin2014AnelasticAO, title={Anelastic Approximation of the Gross-Pitaevskii equation for General Initial Data}, author={Chi-Kun Lin and Kung-Chien Wu}, journal={arXiv: Analysis of PDEs}, year={2014} }

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 $\eps\to 0$, 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…

## One Citation

Asymptotic limit of the Gross-Pitaevskii equation with general initial data

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This paper mainly concerns the mathematical justification of the asymptotic limit of the Gross-Pitaevskii equation with general initial data in the natural energy space over the whole space. We give…

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