ON A CLASS OF STOCHASTIC PARTIAL-DIFFERENTIAL EQUATIONS RELATED TO TURBULENT TRANSPORT

We consider the Cauchy problem for the mass density rho of particles w hich diffuse in an incompressible fluid. The dynamical behaviour of rh o is modeled by a linear, uniformly parabolic differential equation co ntaining a stochastic vector field. This vector field is interpreted a s the velocity field of the fluid in a state of turbulence. Combining a contraction method with techniques from white noise analysis we prov e an existence and uniqueness result for the solution rho is an elemen t of C-1,C-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 clas sical random field, i.e. rho(t,x) is an L-2-random variable for all ti me and space parameters (t,x) is an element of [0, T] x R-d.