Global smooth solutions to Navier-Stokes equations with large initial data in critical space

Abstract

In this paper, we investigate the existence of a unique global smooth solution to the three-dimensional incompressible Navier-Stokes equations and provide a concise proof. We establish a new global well-posedness result that allows the initial data to be arbitrarily large within the critical space ${\dot{B}}_{\infty ,\infty }^{-1}$, while still satisfying the nonlinear smallness condition.