{
  "id": "math/0509354",
  "version": "v1",
  "published": "2005-09-15T16:17:00.000Z",
  "updated": "2005-09-15T16:17:00.000Z",
  "title": "Two-dimensional incompressible viscous flow around a small obstacle",
  "authors": [
    "D. Iftimie",
    "M. C. Lopes Filho",
    "H. J. Nussenzveig Lopes"
  ],
  "journal": "Math. Ann. v. 336 (2006), 449-489",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity $\\omega_0$ and the circulation $\\gamma$ of the initial flow around the obstacle. We prove that, if $\\gamma$ is sufficiently small, the limit flow satisfies the full-plane Navier-Stokes system, with initial vorticity $\\omega_0 + \\gamma \\delta$, where $\\delta$ is the standard Dirac measure. The result should be contrasted with the corresponding inviscid result obtained by the authors in [Comm P.D.E. 28 (2003) 349-379], where the effect of the small obstacle appears in the coefficients of the PDE and not only on the initial data. The main ingredients of the proof are $L^p-L^q$ estimates for the Stokes operator in an exterior domain, a priori estimates inspired on Kato's fixed point method, energy estimates, renormalization and interpolation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-15T16:17:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D05"
    ],
    "keywords": [
      "two-dimensional incompressible viscous flow",
      "initial vorticity",
      "limit flow satisfies",
      "full-plane navier-stokes system",
      "katos fixed point method"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9354I"
    }
  }
}