{"paper":{"title":"Sharp asymptotics for small data solutions of the Vlasov-Nordstr\\\"om system in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.AP","authors_text":"David Fajman, Jacques Smulevici, J\\'er\\'emie Joudioux","submitted_at":"2017-04-18T14:24:44Z","abstract_excerpt":"This paper proves almost-sharp asymptotics for small data solutions of the Vlasov-Nordstr\\\"om system in dimension three. This system consists of a wave equation coupled to a transport equation and describes an ensemble of relativistic, self-gravitating particles. We derive sharp decay estimates using a variant of the vector-field method introduced in previous work. More precisely, we construct modified vector fields, depending on the solutions, to propagate $L^1$-bounds for the distribution function and its derivatives. The modified vector fields are designed to have improved commutation prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05353","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"}