Quantitative regularity theory of the Navier-Stokes equations in critical spaces

Stan Palasek, IAS
Fine Hall 314

Suppose u solves the incompressible Navier-Stokes equations on R^d and is bounded by a constant C in some critical space (e.g., L^d) uniformly in time. In this talk we discuss the problem of controlling the solution's regularity explicitly in terms of C, which can shed new light on qualitative regularity theorems such as that of Escauriaza-Seregin-Sverak and potential blow-up phenomena.

This work is partly joint with Wojciech Ozanski.