Global Existence Theorem for the Solutions of 3d Navier-Stokes System on T3 for small initial data from the space P(a)

TL;DR

This paper proves a global existence theorem for solutions to the 3D Navier-Stokes equations on a torus with small initial data in the pseudomeasure space, analyzing the asymptotic behavior of perturbation series coefficients.

Contribution

It establishes a global existence result for small initial data in the pseudomeasure space and examines the asymptotic behavior of the solution's perturbation series.

Findings

Global existence for small initial data in P(a) space

Asymptotic analysis of perturbation series coefficients

Behavior of solutions on the 3D torus

Abstract

We consider 3d Navier-Stokes system with periodic boundary conditions for small initial data from the space of Pseudomeasures. We provide asymptotic behavior for the coefficients in the perturbation series for the solution of this system.