  In this paper we give local curvature estimates for the Laplacian flow on
closed G_2-structures under the condition that the Ricci curvature is bounded
along the flow. The main ingredient consists of the idea of
Kotschwar-Munteanu-Wang who gave local curvature estimates for the Ricci flow
on complete manifolds and then provided a new elementary proof of Sesum's
result, and the particular structure of the Laplacian flow on closed
G_2-structures. As an immediate consequence, this estimates give a new proof of
Lotay-Wei's result which is an analogue of Sesum's theorem. The second result
is about an interesting evolution equation for the scalar curvature of the
Laplacian flow of closed G_2-structures. Roughly speaking, we can prove that
the time derivative of the scalar curvature R_t is equal to the Laplacian of
R_t, plus an extra term which can be written as the difference of two
nonnegative quantities.
