THE EXISTENCE OF THE EFFECTIVE DIFFUSIVITY TENSOR FOR
DIFFUSIONS WITH INCOMPRESSIBLE MIXING DRIFTS
T. Komorowski
P. Widelski
Abstract: In the present article we consider a model of motion of a passive tracer particle
under a random, non-steady (time dependent), incompressible velocity flow in a medium with
positive molecular diffusivity. We show the existence of the effective diffusivity tensor for the
flow provided that its relaxation time is sufficiently small. In contrast to the previous papers
[23], [6], [20] we do not assume the existence of the stationary and integrable stream matrix
for the flow.
2000 AMS Mathematics Subject Classification: Primary 60F17, 35F27; Secondary
60G44.
Key words and phrases: Random field, diffusions in random media, mixing.