{
  "annotation_id": "483f2a7f-6f61-4278-9b2a-849d7a73e353",
  "date_created": "2026-02-17T05:53:24.223000Z",
  "date_modified": "2026-02-17T05:53:24.223000Z",
  "file_hash": "5155f23509197859706c805bfd6d8184ae725a093229025dd4ecb667f1792aa5",
  "private": false,
  "record": {
    "abstract": "Singular stochastic partial differential equations informally refer to the partial differential equations with rough random force that leads to the products in the nonlinear terms becoming ill-defined. Besides the theories of regularity structures and paracontrolled distributions, the technique of convex integration has emerged as a possible approach to construct a solution to such singular stochastic partial differential equations. We review recent developments in this area, and also demonstrate that an application of the convex integration technique to prove non-uniqueness seems unlikely for a particular singular stochastic partial differential equation, specifically the $\\Phi^{4}$ model from quantum field theory.",
    "arxiv_id": "2601.09990",
    "authors": [
      "Hongjie Dong",
      "Kazuo Yamazaki"
    ],
    "categories": [
      "math.PR",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Remarks on the convex integration technique applied to singular stochastic partial differential equations",
    "url": "https://arxiv.org/abs/2601.09990",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d16b20fc-d775-483f-ba9b-62c9f5f1362a",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}