Global Solution for the incompressible Navier-Stokes equations] { Global Solution for the incompressible Navier-Stokes equations with a class of large data in $BMO^{-1}(\mathbb{R}^3)$

TL;DR

This paper proves the global existence and analyticity of solutions to the incompressible Navier-Stokes equations for a broad class of large initial data in a specific function space, extending previous results limited to small data.

Contribution

It establishes the global well-posedness and analyticity of Navier-Stokes solutions for large initial data in $BMO^{-1}( ^3)$, improving upon classical small data results.

Findings

Proves global well-posedness for large data in $BMO^{-1}( ^3)$

Shows space-time analyticity of solutions

Extends classical results of Koch & Tataru to larger data classes

Abstract

In this paper, we shall establish the global well-posedness, the space-time analyticity of the Navier-Stokes equations for a class of large periodic data $u_0 \in BMO^{-1}(\mathbb{R}^3)$. This improves the classical result of Koch \& Tataru \cite{koch-tataru}, for the global well-posedness with small initial data $u_0 \in BMO^{-1}(\mathbb{R}^n)$.