{
  "id": "2402.03101",
  "version": "v2",
  "published": "2024-02-05T15:29:28.000Z",
  "updated": "2024-02-19T14:19:07.000Z",
  "title": "A flow approach to the generalized KPZ equation",
  "authors": [
    "Ajay Chandra",
    "Léonard Ferdinand"
  ],
  "comment": "Added a new argument for integrable covariances that allows colored noise in 2+1 dimensions. Made changes to allow for more terms in generalized KPZ equation. Many fixes of typos and notation",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We show that the flow approach of Duch [Duc21] can be adapted to prove local well-posedness for the generalised KPZ equation. The key step is to extend the flow approach so that it can accommodate semilinear equations involving smooth functions of the solution instead of only polynomials - this is accomplished by introducing coordinates for the flow built out of the elementary differentials associated to the equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-02-19T14:19:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "flow approach",
      "generalized kpz equation",
      "accommodate semilinear equations",
      "local well-posedness",
      "elementary differentials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}