Local well-posedness of Kolmogorov's two-equation model of turbulence in fractional Sobolev Spaces

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.