{
  "id": "2408.11678",
  "version": "v1",
  "published": "2024-08-21T14:57:53.000Z",
  "updated": "2024-08-21T14:57:53.000Z",
  "title": "Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs",
  "authors": [
    "Daniel Goodair"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2401.10076",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We extend recent existence and uniqueness results for maximal solutions of SPDEs through an improved blow-up criterion. Whilst the maximal time of existence is typically characterised by blow-up in the energy norm of solutions, we show instead that solutions exist until blow-up in the larger spaces of the variational framework. The result is applied to show that solutions of 2D and 3D Stochastic Navier-Stokes Equations retain the higher order regularity of the initial condition on their time of existence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-21T14:57:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "blow-up criterion",
      "variational framework",
      "nonlinear spdes",
      "3d stochastic navier-stokes equations retain",
      "higher order regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}