|
A note on the zero Mach number limit of compressible Euler equations
Author(s):
Wen-An
Yong
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3079-3085.
MSC (2000):
Primary 35B25, 35L45, 76N10
Posted:
April 20, 2005
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
This note presents a short and elementary justification of the classical zero Mach number limit for isentropic compressible Euler equations with prepared initial data. We also show the existence of smooth compressible flows, with the Mach number sufficiently small, on the (finite) time interval where the incompressible Euler equations have smooth solutions.
References:
-
- 1.
- T. Hagstrom and J. Lorenz, On the stability of approximate solutions of hyperbolic-parabolic systems and the all-time existence of smooth, slightly compressible flows, Indiana Univ. Math. J. 51 (2002), pp. 1339-1387. MR 1948453 (2004h:35188)
- 2.
- T. Kato, Nonstationary flows of viscous and ideal fluids in
 , J. Funct. Anal. 9 (1972), pp. 296-305. MR 0481652 (58:1753) - 3.
- S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Commun. Pure Appl. Math. 34 (1981), pp. 481-524. MR 0615627 (84d:35089)
- 4.
- S. Klainerman and A. Majda, Compressible and incompressible fluids, Commun. Pure Appl. Math. 35 (1982), pp. 629-651. MR 0668409 (84a:35264)
- 5.
- A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Springer, New York, 1984. MR 0748308 (85e:35077)
- 6.
- G. Métivier and S. Schochet, The incompressible limit of the non-isentropic Euler equations, Arch. Rational Mech. Anal. 158 (2001), pp. 61-90. MR 1834114 (2002d:76095)
- 7.
- R. Teman, Local existence of solutions of the Euler equations of incompressible perfect fluids, in Turbulence and the Navier-Stokes equations, Springer, New York, 1976, pp. 184-194. MR 0467033 (57:6902)
- 8.
- W.-A. Yong, Singular perturbations of first-order hyperbolic systems with stiff source terms, J. Differ. Equations 155 (1999), pp. 89-132. MR 1693210 (2000c:35011)
- 9.
- W.-A. Yong, Basic aspects of hyperbolic relaxation systems, in Advances in the Theory of Shock Waves, Birkhäuser, Boston, 2001, pp. 259-305. MR 1842777 (2002g:35136)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
35B25, 35L45, 76N10
Retrieve articles in all Journals with MSC
(2000):
35B25, 35L45, 76N10
Additional Information:
Wen-An
Yong
Affiliation:
IWR, Universität Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany
Email:
yong.wen-an@iwr.uni-heidelberg.de
DOI:
10.1090/S0002-9939-05-08077-9
PII:
S 0002-9939(05)08077-9
Keywords:
Compressible Euler equations,
incompressible limit,
symmetrizable hyperbolic systems,
continuation principle,
energy estimates
Received by editor(s):
June 4, 2004
Posted:
April 20, 2005
Communicated by:
M. Gregory Forest
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org