Self-Similar Smoothing of A Fluid Boundary Corner

Series
PDE Seminar
Time
Tuesday, April 21, 2026 - 3:30pm for 1 hour (actually 50 minutes)
Location
Speaker
Neel Patel – University of Maine
Organizer

The Hele-Shaw problem describes the dynamics of the boundary of a single fluid in porous media. For the nonzero surface tension case, we provide the first proof (to the best of our knowledge) of the existence of solutions that initially have a corner. The main challenge is the analysis of a nonlocal equation whose linearization has coefficients that grow at infinity.