{"paper":{"title":"Global existence and lifespan for semilinear wave equations with mixed nonlinear terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chengbo Wang, Daoyuan Fang, Wei Dai","submitted_at":"2018-10-24T07:57:58Z","abstract_excerpt":"Firstly, we study the equation $\\square u = |u|^{q_c}+ |\\partial u|^p$ with small data, where $q_c$ is the critical power of Strauss conjecture and $p\\geq q_c.$ We obtain the optimal lifespan $\\ln({T_\\varepsilon})\\approx\\varepsilon^{-q_c(q_c-1)}$ in $n=3$, and improve the lower-bound of $T_\\varepsilon$ from $\\exp({c\\varepsilon^{-(q_c-1)}})$ to $\\exp({c\\varepsilon^{-(q_c-1)^2/2}})$ in $n=2$. Then, we study the Cauchy problem with small initial data for a system of semilinear wave equations $\\square u = |v|^q,$ $ \\square v = |\\partial_t u|^p$ in 3-dimensional space with $q<2$. We obtain that thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10232","kind":"arxiv","version":2},"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"}