{"paper":{"title":"A $L^{2}$ to $L^{\\infty}$ approach for the Landau Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hyung Ju Hwang, Jinoh Kim, Yan Guo","submitted_at":"2016-10-17T20:34:10Z","abstract_excerpt":"Consider the Landau equation with Coulomb potential in a periodic box. We develop a new $L^{2}\\rightarrow L^{\\infty }$ framework to construct global unique solutions near Maxwellian with small $L^{\\infty }\\ $norm. The first step is to establish global $L^{2}$ estimates with strong velocity weight and time decay, under the assumption of $L^{\\infty }$ bound, which is further controlled by such $L^{2}$ estimates via De Giorgi's method \\cite{golse2016harnack} and \\cite{mouhot2015holder}. The second step is to employ estimates in $S_{p}$ spaces to control velocity derivatives to ensure uniqueness, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05346","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"}