  In this paper, we study the evolution of $L^2$ one forms under Ricci flow
with bounded curvature on a non-compact Rimennian manifold. We show on such a
manifold that the $L^2$ norm of a smooth one form with compact support is
non-increasing along the Ricci flow with bounded curvature. The $L^{\infty}$
norm is showed to have monotonicity property too. Then we use $L^{\infty}$
cohomology of one forms with compact support to study the singularity model for
the Ricci flow on $S^1\times \mathbb{R}^{n-1}$.
