Generalized solution of some parabolic equations with a random drift

Some stochastic partial differential equations arising from a turbulent transport model are studied using Hida's theory of Brownian functionals. For the spatially homogeneous case, the solutions are constructed as a regular or generalized Brownian functional, depending on a small parameter. The regularity property of such solutions is also determined. However, for the spatially nonhomogeneous equations, only generalized solutions in a series form involving iterated singular Wiener integrals are found.This work was supported in part by NSF Grant DMS-87-02236.