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

Abstract

In this paper, we are concerned with the local existence of strong solutions to the $k-\epsilon$ 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.

23 pages

References in corpus (2)

• Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows
• Global solutions to the three-dimensional full compressible magnetohydrodynamic flows