Study of the higher-order asymptotic behavior of quantum field expansions in the theory of two-dimensional fully developed turbulence

We use a simplified $(0{+}1)$-dimensional theory to develop approaches for studying the higher-order asymptotic behavior of quantum field expansions in the two-dimensional theory of fully developed turbulence. We consider the asymptotic behavior of the correlation function in the small-time limit in the theory of fully developed turbulence and derive and investigate the stationarity equation. We show that the perturbation series in this limit has a finite convergence radius.