Global existence of large solutions to 3-D incompressible Navier-Stokes system

TL;DR

This paper establishes the global existence and uniqueness of solutions to the 3-D incompressible Navier-Stokes equations for large initial data in a scale-invariant space, extending previous results to the entire space.

Contribution

It proves global well-posedness for large initial data in abla-invariant spaces, broadening the class of initial conditions for which solutions exist.

Findings

Global existence of solutions for large data in abla-invariant space

Extension of previous results from domain abla to abla space abla

Unique solutions proven for initial data in abla space

Abstract

This paper proves that the 3-D Navier-Stokes system has a unique global solution under an assumpution on the initial data. That allow the data to be arbitrarily large in the scale invariant space \dot{B}_{\infty,\infty}^{-1}, which contains all the known spaces in which there is a global solution for small data. In particular, this work extends the result of global well-posedness for the "ill-prepared" case in [6] to the full space \mathbb{R}^{3}(in [6] the fluid evolves in domain \mathbb{T}^{2}\times\mathbb{R})