Global strong solvability of the Navier-Stokes equations in exterior domains for rough initial data in critical spaces

TL;DR

This paper establishes the global strong solvability of Navier-Stokes equations in exterior domains for rough initial data within certain critical spaces, extending previous results to larger initial data spaces.

Contribution

It proves global strong solutions exist for rough initial data in critical spaces larger than $L^n_\sigma$ in exterior domains, advancing understanding of Navier-Stokes solvability.

Findings

Global strong solutions are obtained for initial data in larger critical spaces.

The results extend previous well-posedness to rougher initial data.

The study applies to exterior domain problems with smooth boundaries.

Abstract

It is well known that the Navier-Stokes equations have unique global strong solutions for standard domains when initial data are small in $L^n_\sigma$. Global well-posedness has been extended to rough initial data in larger critical spaces. This paper explores the global strong solvability of the smooth exterior domain problem for initial data that is small in some critical spaces larger than $L^n_\sigma$