Well-posedness for a molecular beam epitaxy model

We study a general molecular beam epitaxy (MBE) equation modeling the epitaxial growth of thin films. We show that, in the deterministic case, the associated Cauchy problem admits a unique smooth solution for all time, given initial data in the space X-0 = L-2(R-d) boolean AND W-center dot(1,4)(R-d) with d = 1, 2. This improves a recent result by Ag & eacute;las [1], who established global existence in H-3(R-d). Moreover, we investigate the local existence and uniqueness of solutions in the space X0 for the stochastic MBE equation, with an additive noise that is white in time and regular in the space variable. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).