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INCOMPRESSIBLE LIMIT OF THE NON-ISENTROPIC EULER EQUATIONS
 

Summary: INCOMPRESSIBLE LIMIT OF THE NON-ISENTROPIC
EULER EQUATIONS
THOMAS ALAZARD
Abstract. We study the incompressible limit of classical solutions to
the compressible Euler equations for non-isentropic fluids in a domain
Rd
. We consider the case of general initial data. For a domain
, bounded or unbounded, we first prove the existence of classical so-
lutions 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.
1. Introduction
This work is devoted to the study of the so-called incompressible limit
for classical solutions of the compressible Euler equations for non-isentropic
fluids. We consider the case of a flow in a domain Rd with the solid-wall
boundary condition. After the usual rescalings and changes of variables, see
[14, 18], we are led to analyze a quasilinear hyperbolic system depending on
a small parameter , which is the Mach number,
(1.1)

  

Source: Alazard, Thomas - Département de Mathématiques, Université de Paris-Sud 11

 

Collections: Mathematics