Local existence of strong solutions to the $k-\varepsilon$ model equations for turbulent flows

TL;DR

This paper proves the local existence and uniqueness of strong solutions for the $k-psilon$ turbulence model equations in a bounded domain, assuming positive initial turbulent kinetic energy and density.

Contribution

It establishes the first local existence result for strong solutions to the $k-psilon$ model equations under realistic initial conditions.

Findings

Existence of unique local strong solutions proven.

Solutions exist under positive initial turbulent energy and density.

Provides a mathematical foundation for turbulence modeling analysis.

Abstract

In this paper, we are concerned with the local existence of strong solutions to the $k-\varepsilon$ model equations for turbulent flows in a bounded domain $\Omega$$\subset$ $\mathbb{R}^{3}$. We prove the existence of unique local strong solutions under the assumption that turbulent kinetic energy and the initial density both have lower bounds away from zero.