{"paper":{"title":"Derivation of the Boltzmann equation with moderately soft potentials from a perturbed Nanbu particles system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Samir Salem","submitted_at":"2019-10-04T11:49:51Z","abstract_excerpt":"We derive the 3D spatially homogeneous Boltzmann's equation with moderately soft potentials and singular angular interaction, from an interacting particles system. The collision kernel is of the form $B(z,\\sigma)=|z|^{\\gamma}b\\left( \\frac{z}{|z|}\\cdot \\sigma\\right)$ and for $K>0$, $\\sin(\\theta)b\\left(\\cos(\\theta)\\right)\\sim K\\theta^{-1-\\nu}$, with $\\gamma\\in (-2,-1)$ and $\\nu\\in(1,2)$ satisfying $\\gamma+\\nu>0$. We use at the particle level the regularizing effects of the grazing collisions, in order to control the singularity of the soft potential. This enables to use a classical compactness a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.01883","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.01883/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}