{
  "id": "1909.04651",
  "version": "v1",
  "published": "2019-09-10T17:50:41.000Z",
  "updated": "2019-09-10T17:50:41.000Z",
  "title": "Inviscid limit of vorticity distributions in Yudovich class",
  "authors": [
    "Peter Constantin",
    "Theodore D. Drivas",
    "Tarek M. Elgindi"
  ],
  "comment": "15 pgs",
  "categories": [
    "math.AP",
    "physics.flu-dyn"
  ],
  "abstract": "We prove that given initial data $\\omega_0\\in L^\\infty(\\mathbb{T}^2)$, forcing $g\\in L^\\infty(0,T; L^\\infty(\\mathbb{T}^2))$, and any $T>0$, the solutions $u^\\nu$ of Navier-Stokes converge strongly in $L^\\infty(0,T;W^{1,p}(\\mathbb{T}^2))$ for any $p\\in [1,\\infty)$ to the unique Yudovich weak solution $u$ of the Euler equations. A consequence is that vorticity distribution functions converge to their inviscid counterparts. As a byproduct of the proof, we establish continuity of the Euler solution map for Yudovich solutions in the $L^p$ vorticity topology. The main tool in these proofs is a uniformly controlled loss of regularity property of the linear transport by Yudovich solutions. Our results provide a partial foundation for the Miller--Robert statistical equilibrium theory of vortices as it applies to slightly viscous fluids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-10T17:50:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "yudovich class",
      "inviscid limit",
      "vorticity distribution functions converge",
      "unique yudovich weak solution",
      "yudovich solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}