{
  "id": "2208.03850",
  "version": "v1",
  "published": "2022-08-08T00:10:31.000Z",
  "updated": "2022-08-08T00:10:31.000Z",
  "title": "Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier-Stokes equations outside of an infinite cylinder with a periodic boundary condition",
  "authors": [
    "Hideo Kozono",
    "Yutaka Terasawa",
    "Yuta Wakasugi"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the asymptotic behavior of solutions to the steady Navier-Stokes equations outside of an infinite cylinder in $\\mathbb{R}^3$. We assume that the flow is periodic in $x_3$-direction and has no swirl. This problem is closely related with two-dimensional exterior problem. Under a condition on the generalized finite Dirichlet integral, we give a pointwise decay estimate of the vorticity at the spatial infinity. Moreover, we prove a Liouville-type theorem only from the condition of the generalized finite Dirichlet integral.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-08T00:10:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "35B53",
      "76D05"
    ],
    "keywords": [
      "axisymmetric stationary navier-stokes equations outside",
      "periodic boundary condition",
      "liouville-type theorem",
      "infinite cylinder",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}