{
  "id": "0803.0210",
  "version": "v1",
  "published": "2008-03-03T10:40:36.000Z",
  "updated": "2008-03-03T10:40:36.000Z",
  "title": "Fine properties of self-similar solutions of the Navier-Stokes equations",
  "authors": [
    "Lorenzo Brandolese"
  ],
  "journal": "Arch. Rational Mech. Anal. 192 (2009) 375--401",
  "doi": "10.1007/s00205-008-0149-x",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the solutions of the nonstationary incompressible Navier--Stokes equations in $\\R^d$, $d\\ge2$, of self-similar form $u(x,t)=\\frac{1}{\\sqrt t}U\\bigl(\\frac{x}{\\sqrt t}\\bigr)$, obtained from small and homogeneous initial data $a(x)$. We construct an explicit asymptotic formula relating the self-similar profile $U(x)$ of the velocity field to its corresponding initial datum $a(x)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-03T10:40:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76D05",
      "35Q30"
    ],
    "keywords": [
      "self-similar solutions",
      "fine properties",
      "nonstationary incompressible navier-stokes equations",
      "velocity field",
      "self-similar form"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2009,
      "month": "Jun",
      "volume": 192,
      "number": 3,
      "pages": 375
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009ArRMA.192..375B"
    }
  }
}