{"paper":{"title":"The radiative transfer equation in the forward-peaked regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ricardo Alonso, Weiran Sun","submitted_at":"2014-11-01T19:53:07Z","abstract_excerpt":"In this work we study the radiative transfer equation in the forward-peaked regime in free space. Specifically, it is shown that the equation is well-posed by proving instantaneous regularization of weak solutions for arbitrary initial datum in L1. Classical techniques for hypo-elliptic operators such as averaging lemma are used in the argument. Among the interesting aspect of the proof are the use of the stereographic projection and the presentation of a rigorous expression for the scattering operator given in terms of a fractional Laplace-Beltrami operator on the sphere, or equivalently, a w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0163","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"}