Self-Similar Solutions to the Hele-Shaw Problem with Surface Tension

We consider the Hele-Shaw problem with surface tension in an infinite domain. We prove the existence of a family of self-similar solutions. At $t=0$, these solutions have a corner of angle $\theta$ with $0<\mathrm{\mid }\theta -\pi \mathrm{\mid }\ll 1$, and for $t>0$, the solutions are smooth.