  The main objective of this paper is to establish the null controllability for
the fourth order semilinear parabolic equations with the nonlinearities
involving the state and its gradient up to second order. First of all, based on
optimal control theory of partial differential equations and global Carleman
estimates obtained in \cite{gs} for fourth order parabolic equation with
$L^2(Q)$-external force, we establish the global Carleman estimates for the
$L^2(Q)$ weak solutions of the same system with a low regularity external term
and some linear terms including the derivatives of the state up to second
order. Then we prove the null controllability of the fourth order semilinear
parabolic equations by such global Carleman estimates and the Leray-Schauder's
fixed points theorem.
