{"paper":{"title":"Decay estimates for large velocities in the Boltzmann equation without cutoff","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cl\\'ement Mouhot, Cyril Imbert (DMA), Luis Silvestre","submitted_at":"2018-04-17T09:45:42Z","abstract_excerpt":"We consider solutions $f=f(t,x,v)$ to the full (spatially  inhomogeneous) Boltzmann equation with periodic spatial conditions  $x \\in \\mathbb T^d$, for hard and moderately soft potentials  \\emph{without the angular cutoff assumption}, and under the \\emph{a    priori} assumption that the main hydrodynamic fields, namely the  local mass $\\int\\_v f(t,x,v)$ and local energy $\\int\\_v f(t,x,v)|v|^2$  and local entropy $\\int\\_v f(t,x,v) \\ln f(t,x,v)$, are controlled  along time.  We establish quantitative estimates of  \\emph{propagation} in time of \"pointwise polynomial moments\", i.e.  $\\sup\\_{x,v} f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06135","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"}