Renormalization group in the theory of fully developed turbulence. Problem of the infrared relevant corrections to the Navier–Stokes equation

Within the framework of the RG approach to the theory of fully developed turbulence we consider the problem of possible IR relevant corrections to the Navier–Stokes equation. We formulate an exact criterium of the “actual IR relevance” of the corrections. In accordance with this criterium we verify the IR relevance for certain classes of composite operators. All these operators turn out to be actually IR irrelevant for arbitrary values of the RG expansion parameter $\varepsilon$. This confirms the absence of the crossover and the possibility of extrapolation of the RG results (obtained for asymptotically small values of $\varepsilon$) to the physical range $\varepsilon>2$.