{
  "id": "2308.09220",
  "version": "v1",
  "published": "2023-08-18T00:39:35.000Z",
  "updated": "2023-08-18T00:39:35.000Z",
  "title": "Interior and boundary mixed norm derivative estimates for nonstationary Stokes equations",
  "authors": [
    "Hongjie Dong",
    "Hyunwoo Kwon"
  ],
  "comment": "51 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain weighted mixed norm Sobolev estimates in the whole space for nonstationary Stokes equations in divergence and nondivergence form with variable viscosity coefficients that are merely measurable in time variable and have small mean oscillation in spatial variables in small cylinders. As an application, we prove interior mixed norm derivative estimates for solutions to both equations. We also discuss boundary mixed norm Hessian estimates for solutions to equations in nondivergence form under the Lions boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-18T00:39:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76D03",
      "76D07",
      "35K51",
      "35B45"
    ],
    "keywords": [
      "boundary mixed norm derivative estimates",
      "nonstationary stokes equations",
      "mixed norm hessian estimates",
      "mixed norm sobolev estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}