On analytic solutions to NSE in 3-D torus

TL;DR

This paper proves the existence of fully analytic solutions to the Navier-Stokes equations with $H^1$ initial conditions on a 3D torus, advancing understanding of solution regularity.

Contribution

It establishes the existence of analytic solutions to 3D NSE with $H^1$ initial data, a novel regularity result for these equations.

Findings

Existence of solutions analytic in all variables.

Applicable to initial conditions in $H^1$ space.

Advances regularity theory for 3D NSE.

Abstract

We consider NSE with $H^1$-initial conditions on the 3-dimensional torus and prove that there exists a solution that is analytic in all variables.