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

TL;DR

This paper proves the existence of unique global smooth solutions to the 3D Navier-Stokes equations for large initial data in a critical space, advancing understanding of fluid dynamics under broad initial conditions.

Contribution

It establishes a new global well-posedness result for Navier-Stokes equations allowing large initial data in a critical space, with a concise proof.

Findings

Existence of unique global smooth solutions for large initial data

Global well-posedness in the critical space $ ext{dot}B^{-1}_{ ext{infty}, ext{infty}}$

Solution stability under nonlinear smallness condition

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 $\dot{B}^{-1}_{\infty,\infty}$, while still satisfying the nonlinear smallness condition.