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

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.