{"paper":{"title":"A note on intermittency for the fractional heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Conus, Raluca Balan","submitted_at":"2013-10-31T20:15:29Z","abstract_excerpt":"The goal of the present note is to study intermittency properties for the solution to the fractional heat equation $$\\frac{\\partial u}{\\partial t}(t,x) = -(-\\Delta)^{\\beta/2} u(t,x) + u(t,x)\\dot{W}(t,x), \\quad t>0,x \\in \\bR^d$$ with initial condition bounded above and below, where $\\beta \\in (0,2]$ and the noise $W$ behaves in time like a fractional Brownian motion of index $H>1/2$, and has a spatial covariance given by the Riesz kernel of index $\\alpha \\in (0,d)$. As a by-product, we obtain that the necessary and sufficient condition for the existence of the solution is $\\alpha<\\beta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0023","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"}