{
  "id": "2212.11257",
  "version": "v1",
  "published": "2022-12-21T18:39:10.000Z",
  "updated": "2022-12-21T18:39:10.000Z",
  "title": "On the 3D Navier-Stokes Equations with a Linear Multiplicative Noise and Prescribed Energy",
  "authors": [
    "Stefanie Elisabeth Berkemeier"
  ],
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "For a prescribed deterministic kinetic energy we use convex integration to construct analytically weak and probabilistically strong solutions to the 3D incompressible Navier-Stokes equations driven by a linear multiplicative stochastic forcing. These solutions are defined up to an arbitrarily large stopping time and have deterministic initial values, which are part of the construction. Moreover, by a suitable choice of different kinetic energies which coincide on an interval close to time 0, we obtain non-uniqueness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-21T18:39:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d navier-stokes equations",
      "linear multiplicative noise",
      "prescribed energy",
      "3d incompressible navier-stokes equations driven",
      "deterministic initial values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}