Stability of transonic shock fronts in two-dimensional Euler systems
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- by Shuxing Chen
- Trans. Amer. Math. Soc. 357 (2005), 287-308
- DOI: https://doi.org/10.1090/S0002-9947-04-03698-0
- Published electronically: August 19, 2004
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Abstract:
We study the stability of stationary transonic shock fronts under two-dimensional perturbation in gas dynamics. The motion of the gas is described by the full Euler system. The system is hyperbolic ahead of the shock front, and is a hyperbolic-elliptic composed system behind the shock front. The stability of the shock front and the downstream flow under two-dimensional perturbation of the upstream flow can be reduced to a free boundary value problem of the hyperbolic-elliptic composed system. We develop a method to deal with boundary value problems for such systems. The crucial point is to decompose the system to a canonical form, in which the hyperbolic part and the elliptic part are only weakly coupled in their coefficients. By several sophisticated iterative processes we establish the existence and uniqueness of the solution to the described free boundary value problem. Our result indicates the stability of the transonic shock front and the flow field behind the shock.References
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Bibliographic Information
- Shuxing Chen
- Affiliation: Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
- Email: sxchen@public8.sta.net.cn
- Received by editor(s): July 23, 2003
- Published electronically: August 19, 2004
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 357 (2005), 287-308
- MSC (2000): Primary 35L65, 35L67, 76N10
- DOI: https://doi.org/10.1090/S0002-9947-04-03698-0
- MathSciNet review: 2098096