{
  "id": "2408.17321",
  "version": "v1",
  "published": "2024-08-30T14:31:01.000Z",
  "updated": "2024-08-30T14:31:01.000Z",
  "title": "Nonstationary Stokes equations on a domain with curved boundary under slip boundary conditions",
  "authors": [
    "Hongjie Dong",
    "Hyunwoo Kwon"
  ],
  "comment": "44 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider nonstationary Stokes equations in nondivergence form with variable viscosity coefficients and Navier slip boundary conditions with slip coefficient $\\alpha$ in a domain $\\Omega$. On the one hand, if $\\alpha$ is sufficiently smooth, then we obtain a priori local regularity estimates for solutions near a curved portion of the boundary of the domain. On the other hand, if $\\alpha$ depends on the curvature of the boundary of the domain, then we obtain local boundary estimates of Hessians of solutions where the right-hand side does not contain the pressure. Our results are new even if the viscosity coefficients are constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-30T14:31:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76D03",
      "76D07",
      "35K51",
      "35B45"
    ],
    "keywords": [
      "nonstationary stokes equations",
      "curved boundary",
      "viscosity coefficients",
      "navier slip boundary conditions",
      "priori local regularity estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}