Global well-posedness and large time behavior of epitaxy thin film growth model

Abstract

We consider the global well-posedness and large time behavior of solutions for epitaxy thin film growth model in $\mathbb{R}^{d}$ R d with the dimensional $d\geq 3$ d ≥ 3 . First, using the pure energy method and a standard continuity argument, we prove that there exists a unique global strong solution under the condition that the initial data is sufficiently small. Moreover, we also establish the suitable negative Sobolev norm estimates and obtain the optimal decay rates of the higher-order spatial derivatives of the strong solution.