Random field theory in classical dynamical systems

Abstract: Almost all efforts to develop an analytical theory of turbulence use the Navier-Stokes equations, stochasticly forced with a random gaussian delta-correlated in time forcing term. In 1973, Martin, Rose, and Siggia published a mathematical framework, subsequently improved by several researchers, for fomulating statistical field theories for a very broad range of randomly forced classical dybamical systems, that are first-order in time, and local in time. In this talk we present some of the highlights of the MSR formalism and its application to the Navier-Stokes equations.