{"paper":{"title":"Holder continuity for a drift-diffusion equation with pressure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luis Silvestre, Vlad Vicol","submitted_at":"2011-03-19T07:41:09Z","abstract_excerpt":"We address the persistence of H\\\"older continuity for weak solutions of the linear drift-diffusion equation with nonlocal pressure \\[ u_t + b \\cdot \\grad u - \\lap u = \\grad p,\\qquad \\grad\\cdot u =0 \\] on $[0,\\infty) \\times \\R^{n}$, with $n \\geq 2$. The drift velocity $b$ is assumed to be at the critical regularity level, with respect to the natural scaling of the equations. The proof draws on Campanato's characterization of H\\\"older spaces, and uses a maximum-principle-type argument by which we control the growth in time of certain local averages of $u$. We provide an estimate that does not de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3763","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"}