Geodesic
Global solutions of shock reflection by large-angle wedges for potential flow
Gui-Qiang Chen1 ; Mikhail Feldman2
1 Department of Mathematics<br/>Northwestern University<br/>Evanston, IL 60208-2730<br/>United States<br/>and<br/>Mathematical Institute<br/>University of Oxford<br/>0X1 3LB, Oxford<br/>United Kingdom<br/>and <br/>School of Mathematical Sciences<br/>Fudan University<br/>Shanghai 200433, PRC
2 Department of Mathematics<br/>University of Wisconsin<br/>Madison, WI 53706-1388<br/>United States
Annals of mathematics, Tome 171 (2010) no. 2, pp. 1067-1182.

Voir la notice de l'article provenant de la source Annals of Mathematics website

When a plane shock hits a wedge head on, it experiences a reflection-diffraction process and then a self-similar reflected shock moves outward as the original shock moves forward in time. Experimental, computational, and asymptotic analysis has shown that various patterns of shock reflection may occur, including regular and Mach reflection. However, most of the fundamental issues for shock reflection have not been understood, including the global structure, stability, and transition of the different patterns of shock reflection. Therefore, it is essential to establish the global existence and structural stability of solutions of shock reflection in order to understand fully the phenomena of shock reflection. On the other hand, there has been no rigorous mathematical result on the global existence and structural stability of shock reflection, including the case of potential flow which is widely used in aerodynamics. Such problems involve several challenging difficulties in the analysis of nonlinear partial differential equations such as mixed equations of elliptic-hyperbolic type, free boundary problems, and corner singularity where an elliptic degenerate curve meets a free boundary. In this paper we develop a rigorous mathematical approach to overcome these difficulties involved and establish a global theory of existence and stability for shock reflection by large-angle wedges for potential flow. The techniques and ideas developed here will be useful for other nonlinear problems involving similar difficulties.
DOI : 10.4007/annals.2010.171.1067

Gui-Qiang Chen 1 ; Mikhail Feldman 2

1 Department of Mathematics<br/>Northwestern University<br/>Evanston, IL 60208-2730<br/>United States<br/>and<br/>Mathematical Institute<br/>University of Oxford<br/>0X1 3LB, Oxford<br/>United Kingdom<br/>and <br/>School of Mathematical Sciences<br/>Fudan University<br/>Shanghai 200433, PRC
2 Department of Mathematics<br/>University of Wisconsin<br/>Madison, WI 53706-1388<br/>United States 
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Gui-Qiang Chen; Mikhail Feldman. Global solutions of shock reflection by large-angle wedges for potential flow. Annals of mathematics, Tome 171 (2010) no. 2, pp. 1067-1182. doi : 10.4007/annals.2010.171.1067. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.1067/

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