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arXiv · 2311.16970

Well-posedness for a molecular beam epitaxy model

Louis Emerald·Daniel Oliveira da Silva·Achenef Tesfahun
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Abstract

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 $X_0 = L^{2}(R^{d}) \cap \dot{W}^{1,4}(R^{d})$ with $d = 1, 2$. This improves a recent result by Ag\'elas, who established global existence in $H^{3}(R^{d})$. Moreover, we investigate the local existence and uniqueness of solutions in the space $X_0$ for the stochastic MBE equation, with an additive noise that is white in time and regular in the space variable.

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Louis Emerald, Daniel Oliveira da Silva, Achenef Tesfahun. 2023-11-28. Well-posedness for a molecular beam epitaxy model. https://arxiv.org/abs/2311.16970

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