{"paper":{"title":"Regularity theory and global existence of small data solutions to semi-linear de Sitter models with power non-linearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marcelo Rempel Ebert, Michael Reissig","submitted_at":"2017-03-28T23:29:32Z","abstract_excerpt":"In this paper we study the Cauchy problem for semi-linear de Sitter models with power non-linearity. The model of interest is \\[ \\phi_{tt} - e^{-2t} \\Delta \\phi + n\\phi_t+m^2\\phi=|\\phi|^p,\\quad (\\phi(0,x),\\phi_t(0,x))=(f(x),g(x)),\\] where $m^2$ is a non-negative constant. We study the global (in time) existence of small data solutions. In particular, we show the interplay between the power $p$, admissible data spaces and admissible spaces of solutions (in weak sense, in sense of energy solutions or in classical sense)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09838","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"}