{
  "id": "1207.3255",
  "version": "v1",
  "published": "2012-07-13T14:10:56.000Z",
  "updated": "2012-07-13T14:10:56.000Z",
  "title": "Insensitizing controls for the Navier-Stokes equations",
  "authors": [
    "Mamadou Gueye"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we deal with the existence of insensitizing controls for the Navier-Stokes equations in a bounded domain with Dirichlet boundary conditions. We prove that there exist controls insensitizing the $L^2$ -norm of the observation of the solution in an open subset $\\mathcal{O}$ of the domain, under suitable assumptions on the data. This problem is equivalent to an exact controllability result for a cascade system. First we prove a global Carleman inequality for the linearized Navier-Stokes system with right-hand side, which leads to the null controllability at any time $T>0$. Then, we deduce a local null controllability result for the cascade system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-13T14:10:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "navier-stokes equations",
      "insensitizing controls",
      "local null controllability result",
      "cascade system",
      "dirichlet boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013AnIHP..30..825G"
    }
  }
}