Sep 18, 2020

Regular and Singular Structures in Fluid Dynamics and Differential Geometry

Siran Li, NYU Shanghai

Abstract:

We shall report our recent work on the issue of regularity vs. singularity in two distinct realms: fluid mechanics and analysis on manifolds. By exploring connections between geometric structures and fluid motions, we provide novel insights into several classical problems in geometric analysis and mathematical hydrodynamics. More specifically, we shall discuss our progress on the existence and compactness of isometric immersions of manifolds, regularity criteria for the Navier–Stokes equations, and elliptic estimates on Riemannian manifolds. Throughout these topics, ”wild” spirals and oscillations play a central role in our constructions.

Slides for the talk (click)

Recorded video for the talk (click)