{"paper":{"title":"Scattering theory for the radial $\\dot H^{1/2}$-critical wave Equation with a cubic convolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Jiqiang Zheng, Junyong Zhang","submitted_at":"2015-09-30T11:25:10Z","abstract_excerpt":"In this paper, we study the global well-posedness and scattering for the wave equation with a cubic convolution $\\partial_{t}^2u-\\Delta u=\\pm(|x|^{-3}\\ast|u|^2)u$ in dimensions $d\\geq4$. We prove that if the radial solution $u$ with life-span $I$ obeys $(u,u_t)\\in L_t^\\infty(I;\\dot H^{1/2}_x(\\mathbb R^d)\\times\\dot H^{-1/2}_x(\\mathbb R^d))$, then $u$ is global and scatters. By the strategy derived from concentration compactness, we show that the proof of the global well-posedness and scattering is reduced to disprove the existence of two scenarios: soliton-like solution and high to low frequenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09126","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"}