{
  "id": "2004.09172",
  "version": "v1",
  "published": "2020-04-20T09:56:40.000Z",
  "updated": "2020-04-20T09:56:40.000Z",
  "title": "Exact controllability in minimal time of the Navier-Stokes periodic flow in a 2D-channel",
  "authors": [
    "Gabriela Marinoschi"
  ],
  "comment": "22 pages, no figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "This work is concerned with the necessary conditions of optimality for a minimal time control problem $(P)$ for the linearized Navier-Stokes periodic flow in a 2D-channel, subject to a boundary input which acts on the transversal component of the velocity. The objective in this problem is the reaching of the laminar regime in a minimum time, as well as its preservation after this time. The determination of the necessary conditions of optimality relies on the analysis of intermediate minimal time control problems $(P_{k})$ for the Fourier modes $\"k\"$ associated to the Navier-Stokes equations and on the proof of the maximum principle for them. Also it is found that one can construct, on the basis of the optimal controllers of problems $(P_{k}),$ a small time called here \\textit{quasi minimal} and a boundary controller which realizes the required objective in $% (P).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-20T09:56:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93B05",
      "93C20",
      "49K20",
      "35Q35"
    ],
    "keywords": [
      "exact controllability",
      "2d-channel",
      "intermediate minimal time control problems",
      "necessary conditions",
      "linearized navier-stokes periodic flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}