{"paper":{"title":"Uniform in $N$ estimates for a Bosonic system of Hartree-Fock-Bogoliubov type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Manoussos G. Grillakis, Matei Machedon","submitted_at":"2018-08-20T13:41:09Z","abstract_excerpt":"We prove local in time, uniform in $N$, estimates for the solutions $\\phi$, $\\Lambda$ and $\\Gamma$ of a coupled system of Hartree-Fock-Bogoliubov type with interaction potential $v_N(x-y) =N^{3 \\beta} v(N^{\\beta}(x-y))$, with $\\beta <1$ and $v$ a Schwartz function (satisfying additional technical requirements). The initial conditions are general functions in a Sobolev-type space, and the expected correlations in $\\Lambda$ develop dynamically in time. As shown in our previous work, as well as the work of J. Chong, (both in the case $\\beta<2/3$), using the conserved quantities of the system of e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06448","kind":"arxiv","version":2},"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"}