{"paper":{"title":"Soliton resolution for the energy critical damped wave equations in the radial case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jingyuan Gu, Lifeng Zhao","submitted_at":"2023-12-22T07:41:13Z","abstract_excerpt":"We consider energy-critical damped wave equation \\begin{equation*} \\partial_{tt}u-\\Delta u+\\alpha \\partial_t u=\\left|u\\right|^{\\frac{4}{D-2}}u \\end{equation*} with radial initial data in dimensions $D\\geq 4$. The equation has a nontrivial radial stationary solution $W$, called the ground state, which is unique up to sign and scale. We prove that any bounded energy norm solution behaves asymptotically as a superposition of the modulated ground states and a radiation term. In the global case, particularly, the solution converges to a pure multi-bubble due to the damping effect."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04115","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.04115/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}