{"paper":{"title":"Upper bounds for the function solution of the homogenuous 2D Boltzmann equation with hard potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"MATHRISK), Vlad Bally (LAMA","submitted_at":"2017-10-02T14:37:54Z","abstract_excerpt":"We deal with $f\\_{t}(dv),$ the solution of the homogeneous $2D$ Boltzmannequation without cutoff. The initial condition $f\\_{0}(dv)$ may be anyprobability distribution (except a Dirac mass). However, for sufficiently hardpotentials, the semigroup has a regularization property (see \\cite{[BF]}):$f\\_{t}(dv)=f\\_{t}(v)dv$ for every $t>0.$ The aim of this paper is to give upperbounds for $f\\_{t}(v),$ the most significant one being of type $f\\_{t}(v)\\leqCt^{-\\eta}e^{-\\left\\vert v\\right\\vert ^{\\lambda}}$ for some $\\eta,\\lambda>0.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00695","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"}