Advances in Differential Equations

Incompressible limit of the nonisentropic Euler equations with the solid wall boundary conditions

Thomas Alazard

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Abstract

We study the zero Mach number limit of classical solutions to the compressible Euler equations for nonisentropic fluids in a domain $\Omega \subset \mathbb R^d$ ($d=2$ or $3$). We consider the case of general initial data. For a domain $\Omega$, bounded or unbounded, we first prove the existence of classical solutions for a time independent of the small parameter. Then, in the exterior case, we prove that the solutions converge to the solution of the incompressible Euler equations.

Article information

Source
Adv. Differential Equations Volume 10, Number 1 (2005), 19-44.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867894

Mathematical Reviews number (MathSciNet)
MR2106119

Zentralblatt MATH identifier
1101.35050

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 35B25: Singular perturbations 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]

Citation

Alazard, Thomas. Incompressible limit of the nonisentropic Euler equations with the solid wall boundary conditions. Adv. Differential Equations 10 (2005), no. 1, 19--44. https://projecteuclid.org/euclid.ade/1355867894.


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