{"paper":{"title":"A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nicolas Fournier","submitted_at":"2017-03-31T12:10:30Z","abstract_excerpt":"We consider the spatially homogeneous Boltzmann equation for hard potentials with angular cutoff. This equation has a unique conservative weak solution $(f_t)_{t\\geq 0}$, once the initial condition $f_0$ with finite mass and energy is fixed. Taking advantage of the energy conservation, we propose a recursive algorithm that produces a $(0,\\infty)\\times\\mathbb{R}^3$ random variable $(M_t,V_t)$ such that $E[M_t {\\bf 1}_{\\{V_t \\in \\cdot\\}}]=f_t$. We also write down a series expansion of $f_t$. Although both the algorithm and the series expansion might be theoretically interesting in that they expl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10874","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"}