{
  "id": "math/0612154",
  "version": "v1",
  "published": "2006-12-06T15:07:24.000Z",
  "updated": "2006-12-06T15:07:24.000Z",
  "title": "Optimal Shape Design for the Time-dependent Navier--Stokes Flow",
  "authors": [
    "Zhiming Gao",
    "Yichen Ma",
    "Hongwei Zhuang"
  ],
  "comment": "22 pages, 5 figures",
  "categories": [
    "math.OC",
    "math.AP"
  ],
  "abstract": "This paper is concerned with the problem of shape optimization of two-dimensional flows governed by the time-dependent Navier-Stokes equations. We derive the structures of shape gradients with respect to the shape of the variable domain for time-dependent cost functionals by using the state derivative with respect to the shape of the fluid domain and its associated adjoint state. Finally we apply a gradient type algorithm to our problem and numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible in low Reynolds number flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-06T15:07:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B37",
      "35Q30",
      "49K40"
    ],
    "keywords": [
      "time-dependent navier-stokes flow",
      "optimal shape design",
      "low reynolds number flow",
      "time-dependent navier-stokes equations",
      "time-dependent cost functionals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12154G"
    }
  }
}