Local in time solution to Kolmogorov's two-equation model of turbulence

TL;DR

This paper establishes the local-in-time existence of solutions for Kolmogorov's two-equation turbulence model in three dimensions using Galerkin approximations and limit estimates.

Contribution

It provides the first proof of local existence for the model in a three-dimensional periodic domain.

Findings

Existence of local-in-time solutions proven.

Galerkin method effectively applied to the turbulence model.

Estimates ensure solutions satisfy the original equations.

Abstract

We prove the existence of local in time solution to Kolmogorov's two-equation model of turbulence in three dimensional domain with periodic boundary conditions. We apply Galerkin method for appropriate truncated problem. Next, we obtain estimates for a limit of approximate solutions to ensure that it satisfies the original problem.