SPD

Abstract

We review results for a model in surface growth of amorphous material. This stochastic PDE seems to have similar properties to the 3D-Navier-Stokes equation, as the uniqueness of weak solutions seems to be out of reach, although it is a scalar equation. Moreover, in numerical simulations the equation seems to be well behaved and exhibits hill formation followed by coarsening. This talk gives an overview about several results for this model. One result presents the existence of a weak martingale solution satisfying energy inequalities and having the Markov property. Furthermore, under non-degeneracy conditions on the noise, any such solution is strong Feller and has a unique invariant measure. We also discuss the case of possible blow up and existence of solutions in critical spaces.