  In this paper, we observe a set of functionals of metrics which are all
decrease under the Calabi flow and have uniform lower bound along the flow,
which give rise to a set of integral estimates on the curvature flow. Using
these estimates, together with weak compactness we obtained in previous papers
[8] and [10], we prove the long term existence and convergence of the Calabi
flow. Thus give a new proof to Chruscial's theorem. The set of simple ideas of
global integral estimates and concentration compactness should have further
implications in other heat flow problems.
