On the singular incompressible limit of inviscid compressible fluids
type: Item
instance of: scholarly article
title: On the singular incompressible limit of inviscid compressible fluids
zbMATH Open document ID: 0965.35127
DOI: 10.1007/PL00000948
author: Paolo Secchi
published in: Journal of Mathematical Fluid Mechanics
publication date: 2001-07-22T00:00:00Z
review text: The author studies the convergence properties of solutions to the compressible inviscid Euler equations when the Mach number \(\lambda^{-1}\) (which measures the compressibility) goes to zero. It is assumed that the initial velocity is bounded in \(H^3\) and the initial pressure decays like \(\lambda^{-1}\) in \(H^3\). The result is then that the solution exists in \(H^3\) for a time interval \(T\) independent of \(\lambda\), and that one has weak compactness in the limit to the incompressible Euler equations (or strong convergence if one assumes strong convergence of the initial data). The main tool employed is the energy method for symmetric hyperbolic systems. The time regularity deteriorates as \(\lambda\to \infty\) (every time derivative loses a \(\lambda\)) but this turns out not to affect the uniformity of the energy estimates in \(\lambda\).
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q05
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 1484688
zbMATH Keywords: compressible Euler equation
zbMATH Keywords: incompressible Euler equation
zbMATH Keywords: singular incompressible limit
reviewed by: Terence Tao
MaRDI profile type: Publication
full work available at URL: pl00000948
OpenAlex ID: W2028217510
description: scientific article; zbMATH DE number 1484688