{
  "id": "2108.13335",
  "version": "v1",
  "published": "2021-08-30T15:59:16.000Z",
  "updated": "2021-08-30T15:59:16.000Z",
  "title": "A simple construction of the dynamical $Φ^4_3$ model",
  "authors": [
    "Aukosh Jagannath",
    "Nicolas Perkowski"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "The $\\Phi^4_3$ equation is a singular stochastic PDE with important applications in mathematical physics. Its solution usually requires advanced mathematical theories like regularity structures or paracontrolled distributions, and even local well-posedness is highly nontrivial. Here we propose a multiplicative transformation to reduce the periodic $\\Phi^4_3$ equation to a well-posed random PDE. This leads to a simple and elementary proof of global well-posedness, which only relies on Schauder estimates, the maximum principle, and basic estimates for paraproducts, and in particular does not need regularity structures or paracontrolled distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-30T15:59:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple construction",
      "singular stochastic pde",
      "paracontrolled distributions",
      "maximum principle",
      "important applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}