{"paper":{"title":"Global well-posedness for 2D generalized Parabolic Anderson Model via paracontrolled calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Hao Shen, Rongchan Zhu, Xiangchan Zhu","submitted_at":"2024-02-29T13:20:07Z","abstract_excerpt":"This article revisits the problem of global well-posedness for the generalized parabolic Anderson model on $\\mathbb{R}^+\\times \\mathbb{T}^2$ within the framework of paracontrolled calculus \\cite{GIP15}. The model is given by the equation:\n  \\begin{equation*}\n  (\\partial_t-\\Delta) u=F(u)\\eta\n  \\end{equation*}\n  where $\\eta\\in C^{-1-\\kappa}$ with $1/6>\\kappa>0$, and $F\\in C_b^2(\\mathbb{R})$. Assume that $\\eta\\in C^{-1-\\kappa}$ and can be lifted to enhanced noise, we derive new a priori bounds. The key idea follows from the recent work\n  \\cite{CFW24} by A.Chandra, G.L. Feltes and H.Weber to repre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.19137","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.19137/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}