  Let the interface between two immiscible fluids in a Hele-Shaw cell have, at
t=0, a wedge shape. As a wedge is scale-free, the fluid relaxation dynamics are
self-similar. We find the dynamic exponent of this self-similar flow and show
that the interface shape is given by the solution of an unusual inverse problem
of potential theory. We solve this inverse problem analytically for an almost
flat wedge, and numerically otherwise. The wedge solution is useful for
analysis of pinch-off singularities.

Fluid Dynamics;Pattern Formation and Solitons