We consider a particle undergoing Brownian motion in Euclidean space of any dimension, forced by Gaussian random velocity field that is white time and smooth space. show conditional on the field, quenched density after long can be approximated pointwise product deterministic spacetime-stationary $U$. If additionally assumed to incompressible, then $U\equiv 1$ almost surely we obtain local centr...

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...