Analyticité locale pour les solutions de l'équation d'Euler. (Local analyticity for the solutions of Euler's equation)
type: Item
instance of: scholarly article
title: Analyticité locale pour les solutions de l'équation d'Euler. (Local analyticity for the solutions of Euler's equation)
zbMATH Open document ID: 0635.35013
DOI: 10.1007/BF00281084
author: Daniel Le Bail
published in: Archive for Rational Mechanics and Analysis
publication date: 1986-01-01T00:00:00Z
review text: The author considers the Euler equations for non viscous incompressible fluids with non constant density. The flow is contained in an open bounded subset \(\Omega\) of \({\mathbb{R}}^ n\) with analytical boundary. The local analyticity of the solution up to the boundary is studied. More precisely, given a point \(x_ 0\in \partial \Omega\), set \(\gamma_ T(x_ 0)=\{(t,\phi_{t,0}(x_ 0))\), \(t\in [0,T]\}\), where \(\phi_{t,0}(x_ 0)\) is the position at time t of the particle which is in \(x_ 0\) at time \(t=0\) (the solution is known to exist up to time T). Since the velocity field is tangential on the boundary, \(\phi_{t,0}(x_ 0)\in \partial \Omega\). If the solution at time \(t=0\) is analytical up to the boundary near \(x_ 0\), and the external force field is analytical up to the boundary near \(\gamma_ T(x_ 0)\), then the solution is analytical up to the boundary near \(\gamma_ T(x_ 0)\).
Mathematics Subject Classification ID: 35F30
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 76B99
zbMATH DE Number: 4034195
zbMATH Keywords: Euler equations
zbMATH Keywords: non viscous incompressible fluids
zbMATH Keywords: analytical boundary
zbMATH Keywords: local analyticity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4034195