Large data analysis for Kolmogorov's two-equation model of turbulence

TL;DR

This paper proves the existence of weak solutions for Kolmogorov's two-equation turbulence model in three-dimensional flows with diverse boundary conditions, supporting its mathematical robustness and potential applications.

Contribution

It establishes long-time existence of weak solutions for a complex turbulence model with generalized boundary conditions, including slip mechanisms.

Findings

Existence of suitable weak solutions for the model.

Robustness of results under various boundary conditions.

Applicability to complex unsteady flows.

Abstract

We establish long-time and large-data existence of a suitable weak solution to three-dimensional internal unsteady flows described by Kolmogorov's two-equation model of turbulence. The governing system of equations is completed by initial and boundary conditions; concerning the velocity we consider generalized stick-slip boundary conditions. The fact that the admissible class of boundary conditions includes various types of slipping mechanisms on the boundary makes the result robust from the point of view of possible applications.