Differential Geometry Meets Continuum Mechanics: Singularity vs. Regularity Properties of Several Nonlinear PDEs in Physics

Speaker: Siran Li

Location: Warren Weaver Hall 1314

Date: Feb. 26, 2020, 4:15 p.m.

In this talk we report our recent works on nonlinear PDE 
systems arising from elasticity, fluid dynamics, and harmonic maps. Our discussion focuses on the influence of geometrical structures inherent to the physical systems on the analytic properties of the corresponding PDE solutions, especially the regularity/singularity properties. On the other hand, oscillatory and spiraling patterns in these physical systems serve as building blocks for the solution to several questions in global analysis, including the compactness of 
immersed hypersurfaces with critical extrinsic geometry and the Calderon--Zygmund estimates on open manifolds. These applications will also be discussed.