  In this paper, we are concerned with the instability problem of a 3-D
transonic oblique shock wave for the steady supersonic flow past an infinitely
long sharp wedge. The flow is assumed to be isentropic and irrotational. It was
indicated in pages 317 of [9] that if a steady supersonic flow comes from minus
infinity and hits a sharp symmetric wedge, then it follows from the
Rankine-Hugoniot conditions and the physical entropy condition that there
possibly appear a weak shock or a strong shock attached at the edge of the
sharp wedge, which corresponds to a supersonic shock or a transonic shock,
respectively. The question arises which of the two actually occurs. It has
frequently been stated that the strong one is unstable and that, therefore,
only the weak one could occur. However, a convincing proof of this instability
has apparently never been given. The aim of this paper is to understand such a
longstanding open question. We will show that the attached 3-D transonic
oblique shock problem is overdetermined, which implies that the 3-D transonic
shock is unstable in general.
