Regularity and decay estimates of the Navier-Stokes equations

Abstract

In this talk, I will take the mild solution approach to obtain regularity and decay estimates of the incompressible Navier-Stokes equation. I will first introduce the notion of mild solution, and will explain how to obtain analyticity of mild solutions and how to use this regularity to obtain decay rates of weak solutions. I will finally show Log-Lipschitz regularity of mild solutions and Holder regularity of the corresponding flow map.