Global Mild Solutions of the Navier-Stokes Equations

TL;DR

This paper proves the global existence and uniqueness of mild solutions to the 3D incompressible Navier-Stokes equations for initial data in a specific function space, under a norm bound related to viscosity.

Contribution

It establishes the global well-posedness of mild solutions in the space X^{-1} for initial data bounded by the viscosity coefficient, extending previous results.

Findings

Global well-posedness of mild solutions proved

Initial data in X^{-1} space with norm bound by viscosity

Results applicable to three-dimensional incompressible Navier-Stokes equations

Abstract

Here we establish a global well-posedness of \textit{mild} solutions to the three-dimensional incompressible Navier-Stokes equations if the initial data are in the space $\mathcal{X}^{-1}$ defined by $(1.3)$ and if the norms of the initial data in $\mathcal{X}^{-1}$ are bounded exactly by the viscosity coefficient $\mu$.