Filamentations of vortex caps for the Euler equation

Series
Math Physics Seminar
Time
Friday, September 26, 2025 - 11:00am for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gian Marco Marin – Georgia Tech – gmarin8@gatech.edu
Organizer
Matthew Powell

We rigorously prove the filamentation phenomenon for a class of weak solutions to the Euler equations known as vortex caps. Vortex caps are characteristic functions representing time-evolving sets of Lagrangian type, with energy preserved at all times. The filamentation of vortex caps is characterized by L^1 -stability alongside unbounded growth of the perimeter of their interfaces. We recall the existence and stability results for vortex caps on the sphere, based on Yudovich theory. Using L^1 -stability, we derive a lower bound for the growth of the perimeter of vortex caps over time.