{
  "id": "1504.08143",
  "version": "v1",
  "published": "2015-04-30T09:41:22.000Z",
  "updated": "2015-04-30T09:41:22.000Z",
  "title": "On $L^{3,\\infty}$-stability of the Navier-Stokes system in exterior domains",
  "authors": [
    "Hajime Koba"
  ],
  "comment": "53pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper studies the stability of a stationary solution of the Navier-Stokes system with a constant velocity at infinity in an exterior domain. More precisely, this paper considers the stability of the Navier-Stokes system governing the stationary solution which belongs to the weak $L^3$-space $L^{3,\\infty}$. Under the condition that the initial datum belongs to a solenoidal $L^{3 , \\infty}$-space, we prove that if both the $L^{3,\\infty}$-norm of the initial datum and the $L^{3,\\infty}$-norm of the stationary solution are sufficiently small then the system admits a unique global-in-time strong $L^{3,\\infty}$-solution satisfying both $L^{3,\\infty}$-asymptotic stability and $L^\\infty$-asymptotic stability. Moreover, we investigate $L^{3,r}$-asymptotic stability of the global-in-time solution. Using $L^p$-$L^q$ type estimates for the Oseen semigroup and applying an equivalent norm on the Lorentz space are key ideas to establish both the existence of a unique global-in-time strong (or mild) solution of our system and the stability of our solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-30T09:41:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30"
    ],
    "keywords": [
      "navier-stokes system",
      "exterior domain",
      "unique global-in-time strong",
      "stationary solution",
      "asymptotic stability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150408143K"
    }
  }
}