A Solution of the Cauchy Problem for the Loop Equation in Turbulence

Abstract

Under certain conditions, imposed on the viscosity of the fluid, initial data and the class of contours under consideration, the Cauchy problem with finite values of time for the loop equation in turbulence with Gaussian random forces is solved by making use of the smearing procedure for the loop space functional Laplacian. The solution obtained depends on the initial data and its functional derivatives and on the potential of the random forces.