On the existence of global‐in‐time weak solutions and scaling laws for Kolmogorov's two‐equation model for turbulence

This paper is concerned with Kolmogorov's two-equation model for turbulence in R 3 $\mathbb {R}^3$ involving the mean velocity u, pressure p, an average frequency ω > 0 $\omega >0$ , and a turbulent kinetic energy k. We consider system space-periodic boundary conditions cube Ω = ( ] [ ) $\Omega =({]0,a[}){}^3$ which good choice studying decay of free motion sufficiently far away from boundaries. In particular, this compatible rich set similarity transformations turbulence. The main part work consists proving existence global weak solutions model. For we approximate by adding suitable regularizing r-Laplacian invoke result evolutionary equations pseudo-monotone operators. An important point constitutes derivation pointwise priori estimates (upper lower) k (only that are independent box size a, thus allow us to control parabolicity diffusion