{
  "id": "2208.14584",
  "version": "v1",
  "published": "2022-08-31T01:08:28.000Z",
  "updated": "2022-08-31T01:08:28.000Z",
  "title": "Anisotropically weighted $L^q$-$L^r$ estimates of the Oseen semigroup in exterior domains, with applications to the Navier-Stokes flow past a rigid body",
  "authors": [
    "Tomoki Takahashi"
  ],
  "comment": "77 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the spatial-temporal behavior of the Navier-Stokes flow past a rigid body in $\\mathbb{R}^3$. The present paper develops analysis in Lebesgue spaces with anisotropic weights $(1+|x|)^\\alpha(1+|x|-x_1)^\\beta$, which naturally arise in the asymptotic structure of fluid when the translational velocity of the body is parallel to the $x_1$-direction. We derive anisotropically weighted $L^q$-$L^r$ estimates for the Oseen semigroup in exterior domains. As applications of those estimates, we study the stability/attainability of the Navier-Stokes flow in anisotropically weighted $L^q$ spaces to get the spatial-temporal behavior of nonstationary solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-31T01:08:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D05"
    ],
    "keywords": [
      "navier-stokes flow past",
      "exterior domains",
      "oseen semigroup",
      "rigid body",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 77,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}