The Hele-Shaw problem models the dynamics of the interface of a single viscous fluid domain in porous media. While the dynamics around a corner on the fluid interface are known in the absence of surface tension, it is less rigorously studied in the presence of surface tension. In this talk, we will demonstrate the existence of self-similar solutions that initially have a corner, but instantaneously smoothen out. Due to surface tension, the differential equation describing the self-similar solution is a third order nonlocal equation of elliptic type with coefficients that grow at infinity, and thus, requires an interesting linear analysis.