On a class of stochastic partial differential equations related to turbulent transport

We consider the Cauchy problem for the mass density rho of particles which diffuse in an incompressible fluid. The dynamical behaviour of rho is modeled by a linear, uniformly parabolic differential equation containing a stochastic vector field. This vector field is interpreted as the velocity field of the fluid in a state of turbulence. Combining a contraction method with techniques from white noise analysis we prove an existence and uniqueness result for the solution rho is an element of C(1,2)([0, T] x R(d), (J)*), which is a generalized random field. For a subclass of Cauchy problems we show that rho actually is a classical random field, i.e. rho(t,x) is an L(2)-random variable for all time and space parameters (t,x) is an element of [0, T] x R(d).