Analysis and Mathematical Physics

Regularity of Vortex and SQG Patches

I will review some recent progress on regularity properties of vortex and SQG patches. In particular, I will present an example of a vortex patch with continuous initial curvature that immediately becomes infinite but returns to $(C^2)$ class at all integer times only without being time periodic. The proof involves derivation of a new system describing the patch evolution in terms of arc-length and curvature. The talk is based on a work joint with Xiaoyutao Luo.

Date & Time

January 18, 2023 | 3:00pm – 4:00pm

Location

Simonyi Hall 101 and Remote Access

Affiliation

Duke University