  In this paper we are concerned with the global existence of smooth solutions
to the turbulent flow equations for compressible flows in $\mathbb{R}^3$. The
global well-posedness is proved under the condition that the initial data are
close to the standard equilibrium state in $H^3$-framework. The proof relies on
energy estimates about velocity, temperature, turbulent kinetic energy and rate
of viscous dissipation. We use several new techniques to overcome the
difficulties from the product of two functions and higher order norms. This is
the first result concerning $k$-$\varepsilon$ model equations.
