{
  "id": "2211.06952",
  "version": "v1",
  "published": "2022-11-13T16:54:43.000Z",
  "updated": "2022-11-13T16:54:43.000Z",
  "title": "Maximal $L^1$-regularity and free boundary problems for the incompressible Navier-Stokes equations in critical spaces",
  "authors": [
    "Takayoshi Ogawa",
    "Senjo Shimizu"
  ],
  "comment": "59 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "Time-dependent free surface problem for the incompressible Navier-Stokes equations which describes the motion of viscous incompressible fluid nearly half-space are considered. We obtain global well-posedness of the problem for a small initial data in scale invariant critical Besov spaces. Our proof is based on maximal $L^1$-regularity of the corresponding Stokes problem in the half-space and special structures of the quasi-linear term appearing from the Lagrangian transform of the coordinate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-13T16:54:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "35R35",
      "76D05",
      "35K20",
      "42B25",
      "42B37"
    ],
    "keywords": [
      "incompressible navier-stokes equations",
      "free boundary problems",
      "critical spaces",
      "regularity",
      "scale invariant critical besov spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}