{"paper":{"title":"A new approach to the creation and propagation of exponential moments in the Boltzmann equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cl\\'ement Mouhot, Irene Gamba (UT, Jos\\'e Alfredo Ca\\~nizo, Ricardo Alonso, USA)","submitted_at":"2012-03-11T19:15:53Z","abstract_excerpt":"We study the creation and propagation of exponential moments of solutions to the spatially homogeneous $d$-dimensional Boltzmann equation. In particular, when the collision kernel is of the form $|v-v_*|^\\beta b(\\cos(\\theta))$ for $\\beta \\in (0,2]$ with $\\cos(\\theta)= |v-v_*|^{-1}(v-v_*)\\cdot \\sigma$ and $\\sigma \\in \\mathbb{S}^{d-1}$, and assuming the classical cut-off condition $ b(\\cos(\\theta))$ integrable in $\\mathbb{S}^{d-1}$, we prove that there exists $a > 0$ such that moments with weight $\\exp(a \\min{t,1} |v|^\\beta)$ are finite for $t>0$, where $a$ only depends on the collision kernel a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2364","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"}