Existence and analyticity of the Lei-Lin solution of the Navier-Stokes equations on the torus

TL;DR

This paper proves the existence and analyticity of Lei-Lin solutions to the 3D Navier-Stokes equations on the torus, improving bounds on the solutions' radius of analyticity using an adapted proof method.

Contribution

It adapts Bae's alternative proof to the periodic setting, providing improved bounds on the radius of analyticity for Lei-Lin solutions.

Findings

Existence of Lei-Lin solutions on the torus.

Enhanced bounds for the radius of analyticity.

Extension of previous proofs to periodic domains.

Abstract

Lei and Lin have recently given a proof of a global mild solution of the three-dimensional Navier-Stokes equations in function spaces based on the Wiener algebra. An alternative proof of existence of these solutions was then developed by Bae, and this new proof allowed for an estimate of the radius of analyticity of the solutions at positive times. We adapt the Bae proof to prove existence of the Lei-Lin solution in the spatially periodic setting, finding an improved bound for the radius of analyticity in this case.