{"paper":{"title":"Probabilistic well-posedness for supercritical wave equation on $\\mathbb{T}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bo Xia, Chenmin Sun","submitted_at":"2015-08-02T13:05:56Z","abstract_excerpt":"In this article, we follow the strategies, listed in \\cite{Burq2011} and \\cite{OhPo}, in dealing with supercritical cubic and quintic wave equations, we obtain that, the equation\n  \\begin{equation*}\n  \\left\\{\n  \\begin{split}\n  &(\\partial^2_t-\\Delta)u+|u|^{p-1}u=0,\\ \\ 3<p<5\n  &\\big(u,\\partial_tu\\big)|_{t=0}=(u_0,u_1)\\in H^{s}\\times H^{s-1}=:\\mathcal{H}^s,\n  \\end{split}\n  \\right.\n  \\end{equation*} is almost surely global well-posed in the sense of Burq and Tzvetkov\\cite{Burq2011} for any $s\\in (\\frac{p-3}{p-1},1)$. The key point here is that $\\frac{p-3}{p-1}$ is much smaller than the critical in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00228","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"}