# American Institute of Mathematical Sciences

February  2009, 23(1&2): 85-114. doi: 10.3934/dcds.2009.23.85

## Stability of transonic shock-fronts in three-dimensional conical steady potential flow past a perturbed cone

 1 Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730 2 Department of Mathematics,, Shanghai Jiaotong University, Shanghai 200240, China

Received  November 2007 Revised  July 2008 Published  September 2008

For an upstream supersonic flow past a straight-sided cone in R3 whose vertex angle is less than the critical angle, a transonic(supersonic-subsonic) shock-front attached to the cone vertex can beformed in the flow. In this paper we analyze the stability oftransonic shock-fronts in three-dimensional steady potential flowpast a perturbed cone. We establish that the self-similar transonicshock-front solution is conditionally stable in structure withrespect to the conical perturbation of the cone boundary and theupstream flow in appropriate function spaces. In particular, it isproved that the slope of the shock-front tends asymptotically to theslope of the unperturbed self-similar shock-front downstream atinfinity.
Citation: Gui-Qiang Chen, Beixiang Fang. Stability of transonic shock-fronts in three-dimensional conical steady potential flow past a perturbed cone. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 85-114. doi: 10.3934/dcds.2009.23.85
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