Geodesic
Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations
Gui-Qiang G. Chen1 orcid ; Jun Chen2 ; Mikhail Feldman3
1Oxford University, UK and Chinese Academy of Sciences, Beijing, China
2Southern University of Science and Technology, Shenzhen, Guangdong, China
3University of Wisconsin, Madison, USA
Interfaces and free boundaries, Tome 19 (2017) no. 4, pp. 591-626

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DOI

The existence, uniqueness, and asymptotic behavior of steady transonic flows past a curved wedge, involving transonic shocks, governed by the two-dimensional full Euler equations are established. The stability of both weak and strong transonic shocks under the perturbation of the upstream supersonic flow and the wedge boundary is proved. The problem is formulated as a one-phase free boundary problem, in which the transonic shock is treated as a free boundary. The full Euler equations are decomposed into two algebraic equations and a first-order elliptic system of two equations in Lagrangian coordinates. With careful elliptic estimates by using appropriate weighted Hölder norms, the iteration map is defined and analyzed, and the existence of its fixed point is established by performing the Schauder fixed point argument. The careful analysis of the asymptotic behavior of the solutions reveals particular characters of the full Euler equations.
DOI : 10.4171/ifb/394
Classification : 35-XX, 53-XX, 76-XX
Mots-clés : Shock wave, free boundary, wedge problem, steady, supersonic, subsonic, transonic, mixed type, composite type, hyperbolic-elliptic, full Euler equations, physical admissible, existence, stability, asymptotic behavior, decay rate

Gui-Qiang G. Chen  1   ; Jun Chen  2   ; Mikhail Feldman  3

1 Oxford University, UK and Chinese Academy of Sciences, Beijing, China
2 Southern University of Science and Technology, Shenzhen, Guangdong, China
3 University of Wisconsin, Madison, USA 
Gui-Qiang G. Chen; Jun Chen; Mikhail Feldman. Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations. Interfaces and free boundaries, Tome 19 (2017) no. 4, pp. 591-626. doi: 10.4171/ifb/394
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     title = {Stability and asymptotic behavior of transonic flows past wedges for the full {Euler} equations},
     journal = {Interfaces and free boundaries},
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     year = {2017},
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     number = {4},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/394/}
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