{"paper":{"title":"Weak solutions to the sharp interface limit of stochastic Cahn-Hilliard equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Huanyu Yang, Rongchan Zhu","submitted_at":"2019-05-21T08:09:05Z","abstract_excerpt":"We study the asymptotic limit, as $\\varepsilon\\searrow 0$, of solutions of the stochastic Cahn-Hilliard equation: $$\n  \\partial_t u^\\varepsilon=\\Delta \\left(-\\varepsilon\\Delta u^\\varepsilon+\\frac{1}{\\varepsilon}f(u^\\varepsilon)\\right)+\\dot{\\mathcal{W}}^\\varepsilon_t, \\\\ $$ where $\\mathcal{W}^\\varepsilon=\\varepsilon^\\sigma W$ or $\\mathcal{W}^\\varepsilon=\\varepsilon^\\sigma W^\\varepsilon$, $W$ is a $Q$-Wiener process and $W^\\varepsilon$ is smooth in time and converges to $W$ as $\\varepsilon\\searrow 0$. In the case that $\\mathcal{W}^\\varepsilon=\\varepsilon^\\sigma W$, we prove that for all $\\sigma>"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09182","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"}