{"paper":{"title":"Minimal regularity solutions of semilinear generalized Tricomi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huicheng Yin (Nanjing Normal University), Ingo Witt (University of G\\\"ottingen), Zhuoping Ruan (Nanjing University)","submitted_at":"2016-08-05T10:18:46Z","abstract_excerpt":"We prove the local existence and uniqueness of minimal regularity solutions $u$ of the semilinear generalized Tricomi equation $\\partial_t^2 u-t^m \\Delta u =F(u)$ with initial data $(u(0,\\cdot), \\partial_t u(0,\\cdot)) \\in \\dot{H^{\\gamma}}(\\mathbb R^n) \\times \\dot{H}^{\\gamma-\\frac2{m+2}}(\\mathbb R^n)$ under the assumption that $|F(u)|\\lesssim |u|^\\kappa$ and $|F'(u)| \\lesssim |u|^{\\kappa -1}$ for some $\\kappa>1$. Our results improve previous results of M. Beals [2] and of ourselves [15-17]. We establish Strichartz-type estimates for the linear generalized Tricomi operator $\\partial_t^2 -t^m \\De"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01826","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"}