{
  "id": "1004.4033",
  "version": "v1",
  "published": "2010-04-23T00:55:29.000Z",
  "updated": "2010-04-23T00:55:29.000Z",
  "title": "Inviscid Limit for Vortex Patches in A Bounded Domain",
  "authors": [
    "Quansen Jiu",
    "Yun Wang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the inviscid limit of the incompressible Navier-Stokes equations in a smooth, bounded and simply connected domain $\\Omega \\subset \\mathbb{R}^d, d=2,3$. We prove that for a vortex patch initial data the weak Leray solutions of the incompressible Navier-Stokes equations with Navier boundary conditions will converge (locally in time for $d=3$ and globally in time for $d=2$) to a vortex patch solution of the incompressible Euler equation as the viscosity vanishes. In view of the results obtained in [1] and [19] which dealt with the case of the whole space, we derive an almost optimal convergence rate $(\\nu t)^{\\frac34-\\varepsilon}$ for any small $\\varepsilon>0$ in $L^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-23T00:55:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35Q31"
    ],
    "keywords": [
      "inviscid limit",
      "vortex patches",
      "bounded domain",
      "incompressible navier-stokes equations",
      "vortex patch initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.4033J"
    }
  }
}