Superdiffusivity of two dimensional lattice gas models

Abstract

It was proved \cite{EMYa, QY} that stochastic lattice gas dynamics converge to the Navier-Stokes equations in dimension $d=3$ in the incompressible limits. In particular, the viscosity is finite. We proved that, on the other hand, the viscosity for a two dimensional lattice gas model diverges faster than $\log \log t$. Our argument indicates that the correct divergence rate is $(\log t)^{1/2}$. This problem is closely related to the logarithmic correction of the time decay rate for the velocity auto-correlation function of a tagged particle.