Navier-Stokes Equations at Critical Regularity

Explore the mathematical analysis of 3D incompressible Navier-Stokes equations in this 58-minute conference talk from the Institute for Advanced Study. Examine solutions bounded in critical spaces, beginning with the globally well-posed nature of small initial data established through classical work by Fujita-Kato and others. Delve into the challenging problem of large data scenarios and discover recent mathematical constructions demonstrating pathological behaviors including non-uniqueness, norm growth, and Type I blow-up phenomena. Learn about cutting-edge research findings developed through collaborative work with A. Cheskidov, M. Coiculescu, and M. Dai, presented as part of the Joint IAS/PU Analysis and Mathematical Physics seminar series.