{"paper":{"title":"On Hydrodynamic Equations at the Limit of Infinitely Many Molecules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jianfei Xue, Nicholas Jacob, Stamatis Dostoglou","submitted_at":"2014-06-06T21:22:31Z","abstract_excerpt":"We show that weak convergence of point measures and $(2+\\epsilon)$-moment conditions imply hydrodynamic equations at the limit of infinitely many interacting molecules. The conditions are satisfied whenever the solutions of the classical equations for $N$ interacting molecules obey uniform in $N$ bounds. As an example, we show that this holds when the initial conditions are bounded and that the molecule interaction, a certain $N$-rescaling of potentials that include all $r^{-p}$ for $1<p$, is weak enough at the initial time. In this case the hydrodynamic equations coincide with the macroscopic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1816","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"}