  We study Kolmogorov's two-equation model of turbulence on $d-$dimensional
torus. First, the local existence of the solution with the initial data from
non-homogeneous fractional Sobolev spaces (Bessel potential spaces) $H^s$ with
$s>\frac{d}{2}$ is proven using energy methods. Next, we show that solutions
are unique in the class of solutions guaranteed by the local existence theorem.
