The incompressible limit and the initial layer of the compressible Euler equation
type: Item
instance of: scholarly article
title: The incompressible limit and the initial layer of the compressible Euler equation
zbMATH Open document ID: 0618.76074
author: Seiji Ukai
published in: Journal of Mathematics of Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: The author considers the Euler equations for isentropic compressible fluid flow in \(R^ n\), \(n\geq 3\), and discuss the limit of solutions as the Mach number \(\lambda\) tends to infinity. In a previous paper, \textit{S. Klainerman} and \textit{A. Majda} [Commun. Pure Appl. Math. 35, 629-651 (1982; Zbl 0478.76091)] considered this same problem; in particular they proved that unique solutions exist for all large \(\lambda\) on the time interval [0,T] independent of \(\lambda\), and that if the initial datum is incompressible, then the solutions converge as \(\lambda \to +\infty\) uniformly on [0,T] to a solution of the incompressible Euler equation. In the present paper the author shows that even if the initial datum is not incompressible, the limit still exists and satisfies the incompressible Euler equation. Due to the development of initial layer, the convergence is not uniform near \(t=0\).
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 4003779
zbMATH Keywords: Euler equations
zbMATH Keywords: isentropic compressible fluid flow
zbMATH Keywords: limit of solutions
zbMATH Keywords: unique solutions
zbMATH Keywords: incompressible Euler equation
zbMATH Keywords: initial layer
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520925
OpenAlex ID: W1643641630
DOI: 10.1215/KJM/1250520925
description: scientific article; zbMATH DE number 4003779