{
  "id": "2412.20125",
  "version": "v1",
  "published": "2024-12-28T12:01:23.000Z",
  "updated": "2024-12-28T12:01:23.000Z",
  "title": "Spatial $C^1$, $C^2$, and Schauder estimates for nonstationary Stokes equations with Dini mean oscillation coefficients",
  "authors": [
    "Hongjie Dong",
    "Hyunwoo Kwon"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish the spatial differentiability of weak solutions to nonstationary Stokes equations in divergence form with variable viscosity coefficients having $L_2$-Dini mean oscillations. As a corollary, we derive local spatial Schauder estimates for such equations if the viscosity coefficient belongs to $C^\\alpha_x$. Similar results also hold for strong solutions to nonstationary Stokes equations in nondivergence form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-28T12:01:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76D07",
      "35B45",
      "35B65",
      "35Q35"
    ],
    "keywords": [
      "nonstationary stokes equations",
      "dini mean oscillation coefficients",
      "local spatial schauder estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}