{"paper":{"title":"Introduction to scattering for radial 3D NLKG below energy norm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Tristan Roy","submitted_at":"2008-09-23T01:28:40Z","abstract_excerpt":"We prove scattering for the radial nonlinear Klein-Gordon equation $ \\partial_{tt} u - \\Delta u + u = -|u|^{p-1} u $ with $5 > p >3$ and data $ (u_{0}, u_{1}) \\in H^{s} \\times H^{s-1} $, $ 1 > s > 1- \\frac{(5-p)(p-3)}{2(p-1)(p-2)} $ if $ 4 \\geq p > 3 $ and $ 1 > s > 1 - \\frac{(5-p)^{2}}{2(p-1)(6-p)}$ if $ 5> p \\geq 4$. First we prove Strichartz-type estimates in $ L_{t}^{q} L_{x}^{r} $ spaces. Then by using these decays we establish some local bounds. By combining these results with a Morawetz-type estimate and a radial Sobolev inequality we control the variation of an almost conserved quantit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3835","kind":"arxiv","version":3},"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"}