Navier-Stokes Equations at Critical Regularity

This talk is concerned with solutions of the 3D incompressible Navier-Stokes equations that are bounded in a critical space. From small initial data, these solutions are known to be globally well-posed due to classical work of Fujita-Kato and others. I will discuss the problem of large data, including recent constructions of pathological behavior such as non-uniqueness, norm growth, and Type I blow-up. This is joint work with A. Cheskidov, M. Coiculescu, and M. Dai.