Location: Gilman 132
When: October 12th at 1:30 p.m.
Title: Recent developments in the Navier-Stokes equation
Abstract: In this presentation, I will discuss recent progress regarding the regularity of the three-dimensional Navier-Stokes equation, a system of partial differential equations that models the behavior of fluids. While the full regularity of the 3D incompressible Navier-Stokes equation remains an outstanding open question, recently there have been significant breakthroughs in the fluid dynamics community. I will present new mathematical tools that provide deeper insights into the partial regularity of the Navier-Stokes equation and general supercritical systems. We derive nonlinear a priori estimates and trace estimates for the 3D incompressible Navier-Stokes equation, which extend the current picture of higher derivative estimates in the mixed norm. Additionally, I will demonstrate an intriguing application to the inviscid limit problem, which questions to what extent ideal fluids can model slightly viscous fluid.
Bio: Jincheng Yang is a Dickson instructor in the Department of Mathematics at The University of Chicago. She completed her Ph.D. in Mathematics at The University of Texas at Austin in spring 2022, under the supervision of Prof. Luis Caffarelli and Prof. Alexis Vasseur. Her thesis was on Partial regularity results for the three-dimensional incompressible Navier-Stokes equation.
Jincheng’s research interests include analysis, partial differential equations, fluid dynamics, especially the incompressible Euler equation and the Navier-Stokes equation. Her research focuses on the regularity, stability/instability, uniqueness/nonuniqueness properties of the solutions.
Zoom link: https://wse.zoom.us/j/94601022340