{"paper":{"title":"Small data scattering of semirelativistic Hartree equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changhun Yang","submitted_at":"2018-06-19T07:57:37Z","abstract_excerpt":"In this paper we study the small data scattering of Hartree type semirelativistic equation in space dimension $3$. The Hartree type nonlinearity is $[V * |u|^2]u$ and the potential $V$ which generalizes the Yukawa has some growth condition. We show that the solution scatters to linear solution if an initial data given in $ H^{s,1}$ is sufficiently small and $s>\\frac14$. Here, $H^{s, 1}$ is Sobolev type space taking in angular regularity with norm defined by $\\|\\varphi\\|_{ H^{s, 1}} = \\|\\varphi\\|_{ H^{s}} + \\|\\nabla_{\\mathbb S} \\varphi\\|_{H^{s}}$. To establish the results we employ the recently"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07087","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"}