Scaling laws and convergence for the advection-diffusion equation

Abstract

In this paper we study the convergence of stochastic processes related to a random partial differential equation (PDE with random coefficients) of heat equation propagation type in a Kolmogorov's random velocity field. Then we are able to improve the results of Avellanda and Majda in the case of "shear-flow" advection-diffusion because we prove a convergence in law of the solution of the RPDE instead of just convergence of the moments.