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Transonic shocks and free boundary problems for the full Euler equations in infinite nozzles
- Source :
-
Journal de Mathematiques Pures et Appliquees . Aug2007, Vol. 88 Issue 2, p191-218. 28p. - Publication Year :
- 2007
-
Abstract
- Abstract: We establish the existence, stability, and asymptotic behavior of transonic flows with a transonic shock for the steady, full Euler equations in two-dimensional infinite nozzles of slowly varying cross-sections. Given a smooth incoming flow that is close to a uniform supersonic state at the entrance, we prove that there exists a transonic flow whose infinite downstream smooth subsonic region is separated by a smooth transonic shock from the upstream supersonic flow. The solution is unique within the class of transonic solutions that are close to the background solution. This problem is approached by a free boundary problem in which the transonic shock is formulated as a free boundary. An iteration scheme for the free boundary is developed and its fixed point is shown to exist, which is a solution of the free boundary problem, by combining some delicate estimates for a second-order nonlinear elliptic equation on a Lipschitz domain. [Copyright &y& Elsevier]
- Subjects :
- *MECHANICAL shock
*BOUNDARY value problems
*EULER characteristic
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00217824
- Volume :
- 88
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal de Mathematiques Pures et Appliquees
- Publication Type :
- Academic Journal
- Accession number :
- 26038332
- Full Text :
- https://doi.org/10.1016/j.matpur.2007.04.008