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

Abstract

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 $\hat{I}¸$ with $0<|\hat{I}¸-\ddot{I}€|\ll 1$, and for $t>0$, the solutions are smooth.

47 pages, updated references, and minor revisions and streamlining of the nonlinear analysis