A nonlinear estimate of the life span of solutions of the three dimensional Navier–Stokes equations

Abstract

The purpose of this article is to establish bounds from below for the life span of regular solutions to the incompressible Navier-Stokes system, which involve norms not only of the initial data, but also of nonlinear functions of the initial data. We provide examples showing that those bounds are significant improvements to the one provided by the classical fixed point argument. One of the important ingredients is the use of a scale-invariant energy estimate.