{
  "id": "2201.05306",
  "version": "v2",
  "published": "2022-01-14T05:15:07.000Z",
  "updated": "2022-04-29T00:07:02.000Z",
  "title": "Maximal $L_p$-$L_q$ regularity for the Stokes equations with various boundary conditions in the half space",
  "authors": [
    "Naoto Kajiwara"
  ],
  "comment": "31 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove resolvent $L_p$ estimates and maximal $L_p$-$L_q$ regularity estimates for the Stokes equations with Dirichlet, Neumann and Robin boundary conditions in the half space. Each solution is constructed by a Fourier multiplier of $x'$-direction and an integral of $x_N$-direction. We decompose the solution such that the symbols of the Fourier multipliers are bounded and holomorphic. We see that the operator norms are dominated by a homogeneous function of order $-1$ for $x_N$-direction. The basis are Weis's operator-valued Fourier multiplier theorem and a boundedness of a kernel operator. We give a new simple approach to get maximal regularity in the half space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-04-29T00:07:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D35",
      "35B45"
    ],
    "keywords": [
      "half space",
      "stokes equations",
      "weiss operator-valued fourier multiplier theorem",
      "robin boundary conditions",
      "maximal regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}