{"paper":{"title":"Global Regularity for Supercritical Nonlinear Dissipative Wave Equations in 3D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Borislav Yordanov, Kyouhei Wakasa","submitted_at":"2016-06-22T10:39:29Z","abstract_excerpt":"The nonlinear wave equation $u_{tt}-\\Delta u +|u_t|^{p-1}u_t=0$ is shown to be globally well-posed in the Sobolev spaces of radially symmetric functions $H^k_{\\rm rad}({\\bf R}^3)\\times H^{k-1}_{\\rm rad}({\\bf R}^3)$ for all $p\\geq 3$ and $k\\geq 3$. Moreover, global $C^\\infty $ solutions are obtained when the initial data are $C_0^\\infty$ and exponent $p$ is an odd integer. The radial symmetry allows a reduction to the one-dimensional case where an important observation of A. Haraux (2009) can be applied, i.e., dissipative nonlinear wave equations contract initial data in $W^{k,q}({\\bf R})\\times"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06886","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"}