In this paper we are concerned with the convergence rate of solutions to the
three-dimensional turbulent flow equations. By combining the Lp-Lq
estimates for the linearized equations and an elaborate energy method, the
convergence rates are obtained in various norms for the solution to the
equilibrium state in the whole space, when the initial perturbation of the
equilibrium state is small in H3-framework. More precisely, the optimal
convergence rates of the solutions and its first order derivatives in
L2-norm are obtained when the Lp-norm of the perturbation is bounded for
some pβ[1,6/5).Comment: 16 page