{"paper":{"title":"L^1 averaging lemma for transport equations with Lipschitz force fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Han-Kwan (DMA)","submitted_at":"2010-11-28T11:15:22Z","abstract_excerpt":"The purpose of this note is to extend the $L^1$ averaging lemma of Golse and Saint-Raymond \\cite{GolSR} to the case of a kinetic transport equation with a force field $F(x)\\in W^{1,\\infty}$. To this end, we will prove a local in time mixing property for the transport equation $\\partial_t f + v.\\nabla_x f + F.\\nabla_v f =0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6032","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"}