Global weak solutions to a sixth order cahn-hilliard type equation

We study a sixth order Cahn-Hilliard type equation that arises as a model for the faceting of a growing surface. We show existence of global-in-time weak solutions in two space dimensions, assuming periodic boundary conditions. We also establish exponential-in-time a priori estimates on the H ³ norm of solutions. These bounds enable us to prove the uniqueness of weak solutions. We also show the regularizing effect of the equation on the data.