Tohoku Mathematical Journal
2002
March
SECOND SERIES VOL. 54, NO. 1

Tohoku Math. J.
54 (2002), 105-120

Title A FREE BOUNDARY VALUE PROBLEM OF EULER SYSTEM ARISING IN SUPERSONIC FLOW PAST A CURVED CONE

Author Shuxing Chen

(Received April 5, 2000, revised July 23, 2001)
Abstract. We study a free boundary value problem of the Euler system arising in the inviscid steady supersonic flow past a symmetric curved cone. The existence and stability of piesewise smooth weak entropy solutions was established, provided the cone is a small perturbation of its tangential cone with a vertex angle less than a given value determined by the parameters of the coming flow. Since the change of the entropy of the flow is also considered, the result in this paper gives a more precise description than previous ones on such problems.

2000 Mathematics Subject Classification. Primary 35L60; Secondary 35L67, 35L45.

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