{
  "id": "math/0503597",
  "version": "v1",
  "published": "2005-03-25T13:55:30.000Z",
  "updated": "2005-03-25T13:55:30.000Z",
  "title": "Global L_2-solutions of stochastic Navier-Stokes equations",
  "authors": [
    "R. Mikulevicius",
    "B. L. Rozovskii"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117904000000630 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2005, Vol. 33, No. 1, 137-176",
  "doi": "10.1214/009117904000000630",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper concerns the Cauchy problem in R^d for the stochastic Navier-Stokes equation \\partial_tu=\\Delta u-(u,\\nabla)u-\\nabla p+f(u)+ [(\\sigma,\\nabla)u-\\nabla \\tilde p+g(u)]\\circ \\dot W, u(0)=u_0,\\qquad divu=0, driven by white noise \\dot W. Under minimal assumptions on regularity of the coefficients and random forces, the existence of a global weak (martingale) solution of the stochastic Navier-Stokes equation is proved. In the two-dimensional case, the existence and pathwise uniqueness of a global strong solution is shown. A Wiener chaos-based criterion for the existence and uniqueness of a strong global solution of the Navier-Stokes equations is established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-25T13:55:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60",
      "76M35"
    ],
    "keywords": [
      "stochastic navier-stokes equation",
      "strong global solution",
      "global strong solution",
      "paper concerns",
      "wiener chaos-based criterion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3597M"
    }
  }
}