Global vortex sheet solutions of Euler equations in the plane
type: Item
instance of: scholarly article
title: Global vortex sheet solutions of Euler equations in the plane
zbMATH Open document ID: 0667.35046
DOI: 10.1016/0022-0396(88)90105-2
author: Jean Duchon
author: Raoul Robert
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: This paper deals with the singular solutions of the Euler equations for an incompressible perfect fluid in the plane. The authors employ a fixed-point technique in order to prove that if the initial vorticity density \(\Omega_ 0\) is not arbitrary but is chosen depending on the initial sheet \(\Gamma_ 0\), the vortex sheet \(\Gamma_ t\) exists for all \(t>0.\) In addition, \(\Gamma_ t\) and \(\Omega\) (t) (the vorticity density at \(t>0)\) become analytic for \(t>0\) and they converge to a straight line and to a constant, respectively, for infinite t.
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 76B47
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4092006
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: singular solutions
zbMATH Keywords: Euler equations
zbMATH Keywords: incompressible perfect fluid
zbMATH Keywords: fixed-point technique
zbMATH Keywords: initial vorticity density
reviewed by: Adrian Carabineanu
MaRDI profile type: Publication
full work available at URL: 0022-0396(88)90105-2
OpenAlex ID: W2094492655
cites work: Q3843473
cites work: Q5518219
cites work: On Commutators of Singular Integrals and Bilinear Singular Integrals
cites work: Finite time analyticity for the two and three dimensional Kelvin- Helmholtz instability
cites work: Q3710185
description: scientific article; zbMATH DE number 4092006