On analyticity of incompressible viscid fluid flow in n-dimensional torus

TL;DR

This paper proves that the Navier-Stokes equations on an n-dimensional torus have a unique, locally time-analytic solution for initial data in distribution space, represented as a global series.

Contribution

It establishes the local-in-time analyticity of solutions to the Navier-Stokes equations in n-dimensional torus for initial data in distribution class, with a global series representation.

Findings

Unique local-in-time analytic solutions exist.

Solutions can be expressed as a global series.

Initial data in distribution class leads to analytic solutions.

Abstract

We prove that the evolutionary Navier-Stokes equation in n-D torus with initial data in the class of distributions has an unique solution (local in t) that is analytic by all variables. This solution presents as a series globally.