Energy dissipation of weak solutions for a surface growth model.

In this paper, we derive the dissipation term in the local energy balance law of weak solutions for a surface growth model arising in the molecular-beam-epitaxy process by using the third-order structure functions. This enables us to address Yang's question posed in [52, J. Differential Equations 283, 2021] , consider generalized Onsager conjecture, and present an upper bound of energy dissipation rate of the form O (ν 3 α − 1 α + 1 ) under the condition that the weak solution h ν belongs to L 3 (0 , T ; B 3 , ∞ α + 1 (T)) with α ∈ (0 , 1) in this model. More importantly, the link between Duchon-Robert's remarkable dissipation term and Lions's classical sufficient condition for energy balance law in the 3D Navier-Stokes equations is illustrated. [ABSTRACT FROM AUTHOR]