{"paper":{"title":"Anelastic Approximation of the Gross-Pitaevskii equation for General Initial Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Chi-Kun Lin, Kung-Chien Wu","submitted_at":"2015-12-01T15:52:07Z","abstract_excerpt":"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 incompressible Euler equations. The resonant effects the singular limit process and it can be overcome "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00310","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}