  The Triple-Deck equations are a classical boundary layer model which
describes the asymptotics of a viscous flow near the separation point, and the
Couette flow is an exact stationary solution to the Triple-Deck equations. In
this paper we prove the local rigidity of the Couette flow in the sense that
there are no other stationary solutions near the Couette flow in a scale
invariant space. This provides a stark contrast to the well-studied stationary
Prandtl counterpart, and in particular offers a first result towards the
rigidity question raised by R. E. Meyer in 1983.
