  In this follow up paper, we focus on the viscous Burgers equation. There,
using the Hopf-Cole transformation, we compute the long time behavior of
solutions for some classes of infinite mass initial datas. We show that an
enhanced dissipation effect occurs generically, that is the decay rate in time
is better than if we considered instead the heat equations for the same inital
value. We also show the existence of a kind of global attractor per class.
