  In this paper we examine well-posedness for a class of fourth-order nonlinear
parabolic equation $\partial_t u + (-\Delta)^2 u = \nabla \cdot F(\nabla u)$,
where $F$ satisfies a cubic growth conditions. We establish existence and
uniqueness of the solution for small initial data in local BMO spaces. In the
cubic case $F(\xi) = \pm \lvert \xi \rvert^2 \xi$ we also examine the large
time behaivour and stability of global solutions for arbitrary and small
initial data in VMO, respectively.
