Global in time solution to Kolmogorov's two-equation model of turbulence with small initial data

TL;DR

This paper proves the existence of a global in time solution for Kolmogorov's two-equation turbulence model in three dimensions, assuming small initial data, advancing the mathematical understanding of turbulence modeling.

Contribution

It establishes the first rigorous proof of global solutions for Kolmogorov's model with small initial data in a three-dimensional setting.

Findings

Existence of global solutions under small initial data

Mathematical validation of Kolmogorov's turbulence model

Advancement in theoretical turbulence modeling

Abstract

We prove the existence of global in time solution to Kolmogorov's two-equation model of turbulence in three dimensional domain with periodic boundary conditions under smallness assumption imposed on initial data.