On the low Mach number limit for the compressible Euler system

0504564 - MÚ 2020 RIV US eng J - Journal Article
Feireisl, Eduard - Klingenberg, Ch. - Markfelder, S.
On the low Mach number limit for the compressible Euler system.
SIAM Journal on Mathematical Analysis. Roč. 51, č. 2 (2019), s. 1496-1513. ISSN 0036-1410. E-ISSN 1095-7154
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : low Mach number limit * compressible Euler system * measure-valued solution
OECD category: Pure mathematics
Impact factor: 1.392, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1137/17M1131799

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.
Permanent Link: http://hdl.handle.net/11104/0296169