C. Landim, S. Olla and H.-T. Yau
First order correction for the hydrodynamic limit
of asymmetric simple exclusion processes in dimension $d\ge 3$.
(388K, ps)
ABSTRACT. It is well known that the hydrodynamic limit of the asymmetric simple exclusion is governed
by a viscousless Burgers equation in the Euler scale [R]. We prove that,
in the same scale,
the next order correction is given by a viscous Burgers equation up to a
fixed time $T$ for dimension
$d \ge 3$, provided that the corresponding viscousless Burger equation
has a smooth solution up to time $T$. The diffusion coefficient was
characterized via a variation of Green-Kubo formula by [V, X, EMY].
Within the framework of asymmetric
simple exclusion, this provides a rigorous verification for the
interpretation of analogous phenomena that the correction to the
Euler equation is given by the Navier--Stokes equation if the time scale is
within the Euler scale.