{
"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"
}
}
}