{"paper":{"title":"Global Hilbert Expansion for the Vlasov-Poisson-Boltzmann System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Juhi Jang, Yan Guo","submitted_at":"2009-10-28T22:38:47Z","abstract_excerpt":"We study the Hilbert expansion for small Knudsen number $\\varepsilon$ for the Vlasov-Boltzmann-Poisson system for an electron gas. The zeroth order term takes the form of local Maxwellian: $ F_{0}(t,x,v)=\\frac{\\rho_{0}(t,x)}{(2\\pi \\theta_{0}(t,x))^{3/2}} e^{-|v-u_{0}(t,x)|^{2}/2\\theta_{0}(t,x)},\\text{\\ }\\theta_{0}(t,x)=K\\rho_{0}^{2/3}(t,x).$ Our main result states that if the Hilbert expansion is valid at $t=0$ for well-prepared small initial data with irrotational velocity $u_0$, then it is valid for $0\\leq t\\leq \\varepsilon ^{-{1/2}\\frac{2k-3}{2k-2}},$ where $\\rho_{0}(t,x)$ and $ u_{0}(t,x)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5512","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"}