Global solutions of two-dimensional Navier-Stokes and Euler equations
type: Item
instance of: scholarly article
title: Global solutions of two-dimensional Navier-Stokes and Euler equations
zbMATH Open document ID: 0837.35110
DOI: 10.1007/BF00387712
author: Matania Ben-Artzi
published in: Archive for Rational Mechanics and Analysis
publication date: 1996-05-19T00:00:00Z
review text: The Cauchy problem for the Navier-Stokes system in \(\mathbb{R}^2\) is considered in the vorticity formulation. A new approach to the existence and uniqueness results based upon comparison principles for linear parabolic equations is proposed. The existence of global solutions to Navier-Stokes (NS) and Euler (E) equations with the initial vorticity in \(L^1(\mathbb{R}^2)\) for (NS) and in \((L^1\cap L^r)(\mathbb{R}^2)\), \(r> 2\), is proved. The solution to (NS) is shown to be unique, smooth and continuously dependent on initial data, and the velocity solution to (E) is Hölder continuous in the space and time coordinates. Another result is the existence of a subsequence of solutions to (NS) converging to a solution of (E) as the viscosity vanishes.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76B47
zbMATH DE Number: 754030
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: Euler equations
zbMATH Keywords: global solutions
zbMATH Keywords: Cauchy problem
zbMATH Keywords: existence and uniqueness results
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00387712
OpenAlex ID: W1986497389
description: scientific article; zbMATH DE number 754030