Publikation: On the Low Mach Number Limit for the Compressible Euler System
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2019
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European Union (EU): 320078
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SIAM Journal on Mathematical Analysis. Society for Industrial & Applied Mathematics (SIAM). 2019, 51(2), S. 1496-1513. ISSN 0036-1410. eISSN 1095-7154. Verfügbar unter: doi: 10.1137/17m1131799
Zusammenfassung
In this paper, we propose a new approach to singular limits of inviscid fluid flows based on the concept of dissipative measure-valued solutions. We show that dissipative measure-valued solutions of the compressible Euler equations converge to the smooth solution of the incompressible Euler system when the Mach number tends to zero. This holds both for well-prepared and ill-prepared initial data, where in the latter case the presence of acoustic waves causes difficulties. However this effect is eliminated on certain unbounded domains and, in particular, on the whole space, thanks to dispersion.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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low Mach number limit, compressible Euler system, measure-valued solution
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FEIREISL, Eduard, Christian KLINGENBERG, Simon MARKFELDER, 2019. On the Low Mach Number Limit for the Compressible Euler System. In: SIAM Journal on Mathematical Analysis. Society for Industrial & Applied Mathematics (SIAM). 2019, 51(2), S. 1496-1513. ISSN 0036-1410. eISSN 1095-7154. Verfügbar unter: doi: 10.1137/17m1131799BibTex
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year={2019},
doi={10.1137/17m1131799},
title={On the Low Mach Number Limit for the Compressible Euler System},
number={2},
volume={51},
issn={0036-1410},
journal={SIAM Journal on Mathematical Analysis},
pages={1496--1513},
author={Feireisl, Eduard and Klingenberg, Christian and Markfelder, Simon}
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<dcterms:abstract>In this paper, we propose a new approach to singular limits of inviscid fluid flows based on the concept of dissipative measure-valued solutions. We show that dissipative measure-valued solutions of the compressible Euler equations converge to the smooth solution of the incompressible Euler system when the Mach number tends to zero. This holds both for well-prepared and ill-prepared initial data, where in the latter case the presence of acoustic waves causes difficulties. However this effect is eliminated on certain unbounded domains and, in particular, on the whole space, thanks to dispersion.</dcterms:abstract>
<dc:contributor>Klingenberg, Christian</dc:contributor>
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