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This paper is concerned with Kolmogorov's two-equation model for the freeturbulence in three dimensions. We first discuss scaling laws for slightly moregeneral two-equation models to highlight the special role of the model devisedby Kolmogorov in 1942. The main part of the paper consists in proving theexistence of weak solutions of Kolmogorov's under space-periodic boundaryconditions in a cube. To this end, we provide new a priori estimates and invokeexistence result for pseudo-monotone operators.

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