  We considered the generalization of Einstein's model of Brownian motion when
the key parameter of the time interval of free jumps degenerates. This
phenomenon manifests in two scenarios: a) flow of the fluid, which is highly
dispersing like a non-dense gas, and b) flow of fluid far away from the source
of flow, when the velocity of the flow is incomparably smaller than the
gradient of the pressure. First, we will show that both types of flows can be
modeled using the Einstein paradigm. We will investigate the question: What
features will particle flow exhibit if the time interval of the free jump is
inverse proportional to the density of the fluid and its gradient ? We will
show that in this scenario, the flow exhibits localization property, namely: if
at some moment of time $t_{0}$ in the region gradient of the pressure or
pressure itself is equal to zero, then for some time T during t interval $[
t_{0}, t_0+T ]$ there is no flow in the region. This directly links to
Barenblatt's finite speed of propagation property for the degenerate equation.
The method of proof is very different from Barenblatt's method and based on
Vespri - Tedeev technique.
