The vanishing viscosity limit of statistical solutions of the Navier- Stokes equations. I: 2-D periodic case
type: Item
instance of: scholarly article
title: The vanishing viscosity limit of statistical solutions of the Navier- Stokes equations. I: 2-D periodic case
zbMATH Open document ID: 0732.35069
DOI: 10.1016/0022-247X(91)90012-O
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: The author studies the family of statistical solutions \(P^{\epsilon}_ t\) (with a common initial data \(P_ 0)\) of the Navier-Stokes equations \(u_ t+(\nabla \cdot u)u+\nabla p=\epsilon \Delta u\), \(\nabla \cdot u=0\) in the 2-dimensional periodic domain with a small viscosity \(\epsilon\). The main result is the strong compactness of the family \(\{P^{\epsilon}_ t|\epsilon \in (0,1]\}\). Thus by choosing a subsequence the author obtains a global in time statistical solution of the Euler equations. The uniqueness remains open. [For part II see the following review.]
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 4210680
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: viscosity
zbMATH Keywords: statistical solution
author: Dongho Chae
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4210680