The zero diffusion limit of 2-D Navier-Stokes equations with \(L^1\) initial vorticity
type: Item
instance of: scholarly article
title: The zero diffusion limit of 2-D Navier-Stokes equations with \(L^1\) initial vorticity
zbMATH Open document ID: 0959.35136
author: Guangrong Wu
author: Ping Zhang
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: The limiting process of vanishing kinematic viscosity \(\nu\) is considered for the pure initial value problem for the incompressible Navier-Stokes equations in \(\mathbb{R}^2\). It is shown that a subsequence of the family of solutions \((v^\nu)_{\nu\in]0,1]}\) converges weakly in \(L^\infty(]0,\infty[, L^2(\mathbb{R}^2))\) to a weak solution \(v^0\) of the limit problem with \(\nu = 0\) (incompressible Euler equation) as \(\nu\to 0+\), provided that the initial data \(v^\nu(0+) =v_0\in L^2(\mathbb{R}^2)\) are such that the vorticity curl \(v_0\) is in \(L^1(\mathbb{R}^2)\).
reviewed by: Rainer Picard
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D09
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 1492589
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: Euler equation
zbMATH Keywords: vorticity
MaRDI profile type: Publication
full work available at URL: dcds.1999.5.631
OpenAlex ID: W40063773
DOI: 10.3934/DCDS.1999.5.631
description: scientific article; zbMATH DE number 1492589