Journal of Statistical Physics, Vol. 115, Nos. 5/6, June 2004. p. 1361-1388.
The trajectories of a passive tracer in a turbulent flow satisfy the ordinary differential equation x'(t) = V(t, x(t)), where V(t, x) is a stationary random field, the so-called Eulerian velocity. It is a nontrivial question to define the dynamics of the tracer in the case when the realizations of the Eulerian field are only spatially Holder regular because the ordinary differential equation in question lacks then uniqueness.