{"paper":{"title":"H\\\"older estimates for fractional parabolic equations with critical divergence free drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Matias G. Delgadino, Scott Smith","submitted_at":"2016-09-09T08:32:39Z","abstract_excerpt":"This work focuses on drift-diffusion equations with fractional dissipation $(-\\Delta)^{\\alpha}$ in the regime $\\alpha \\in (1/2,1)$. Our main result is an a priori H\\\"older estimate on smooth solutions to the Cauchy problem, starting from initial data with finite energy. We prove that for some $\\beta \\in (0,1)$, the $C^{\\beta}$ norm of the solution depends only on the size of the drift in critical spaces of the form $L^{q}_{t}(BMO^{-\\gamma}_{x})$ with $q>2$ and $\\gamma \\in (0,2\\alpha-1]$, along with the $L^{2}_{x}$ norm of the initial datum. The proof uses the Caffarelli/Vasseur variant of De G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02691","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"}