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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Transonic shocks in 3-D compressible flow passing a duct with a general section for Euler systems

Author: Shuxing Chen
Journal: Trans. Amer. Math. Soc. 360 (2008), 5265-5289
MSC (2000): Primary 35L65; Secondary 35L67
Published electronically: April 8, 2008
MathSciNet review: 2415074
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Abstract: This paper is devoted to the study of a transonic shock in three-dimensional steady compressible flow passing a duct with a general section. The flow is described by the steady full Euler system, which is purely hyperbolic in the supersonic region and is of elliptic-hyperbolic type in the subsonic region. The upstream flow at the entrance of the duct is a uniform supersonic one adding a three-dimensional perturbation, while the pressure of the downstream flow at the exit of the duct is assigned apart from a constant difference. The problem to determine the transonic shock and the flow behind the shock is reduced to a free boundary value problem of an elliptic-hyperbolic system. The new ingredients of our paper contain the decomposition of the elliptic-hyperbolic system, the determination of the shock front by a pair of partial differential equations coupled with the three-dimensional Euler system, and the regularity analysis of solutions to the boundary value problems introduced in our discussion.

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Additional Information

Shuxing Chen
Affiliation: School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

Keywords: Transonic shock, Euler system, elliptic-hyperbolic system, compressible flow, multidimensional conservation laws
Received by editor(s): August 10, 2006
Published electronically: April 8, 2008
Additional Notes: The paper was partially supported by the National Natural Science Foundation of China 10531020, the National Basic Research Program of China 2006CB805902 and the Doctorial Foundation of National Educational Ministry 20050246001
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.