3 papers
math.AP2023
Well-posedness for a molecular beam epitaxy model
Louis Emerald, Daniel Oliveira da Silva, Achenef Tesfahun
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…
math.AP2021
Rigorous derivation of the Whitham equations from the water waves equations in the shallow water regime
Louis Emerald
We derive the Whitham equations from the water waves equations in the shallow water regime using two different methods, thus obtaining a direct and rigorous link between these two…
math.AP2020
Rigorous derivation from the water waves equations of some full dispersion shallow water models
Louis Emerald
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formall…