{
  "id": "2107.04495",
  "version": "v1",
  "published": "2021-07-09T15:37:23.000Z",
  "updated": "2021-07-09T15:37:23.000Z",
  "title": "Carleman estimate for the Navier-Stokes equations and applications",
  "authors": [
    "Oleg Y. Imanuvilov",
    "Luca Lorenzi",
    "M. Yamamoto"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "For linearized Navier-Stokes equations, we first derive a Carleman estimate with a regular weight function. Then we apply it to establish conditional stability for the lateral Cauchy problem and finally we prove conditional stability estimates for inverse source problem of determining a spatially varying divergence-free factor of a source term.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-09T15:37:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35R25",
      "35Q30"
    ],
    "keywords": [
      "carleman estimate",
      "applications",
      "regular weight function",
      "lateral cauchy problem",
      "conditional stability estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}