{"paper":{"title":"Can the Stochastic Wave Equation with Strong Drift Hit Zero?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Carl Mueller, Kevin Lin","submitted_at":"2018-02-26T18:10:05Z","abstract_excerpt":"We study the stochastic wave equation with multiplicative noise and singular drift: \\[ \\partial_tu(t,x)=\\Delta u(t,x)+u^{-\\alpha}(t,x)+g(u(t,x))\\dot{W}(t,x) \\] where $x$ lies in the circle $\\mathbf{R}/J\\mathbf{Z}$ and $u(0,x)>0$. We show that\n  (i) If $0<\\alpha<1$ then with positive probability, $u(t,x)=0$ for some $(t,x)$.\n  (ii) If $\\alpha>3$ then with probability one, $u(t,x)\\ne0$ for all $(t,x)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09487","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"}