2 citations · 3 across the 6 of their papers we have counts for
6 papers
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…
Rigorous derivation of weakly dispersive shallow water models with large amplitude topography variations
Louis Emerald, Martin Oen Paulsen
We derive rigorously from the water waves equations new irrotational shallow water models for the propagation of surface waves in the case of uneven topography in horizontal dimens…
Long time well-posedness and full justification of a Whitham-Green-Naghdi system
Louis Emerald, Martin Oen Paulsen
We establish the full justification of a "Whitham-Green-Naghdi" system modeling the propagation of surface gravity waves with bathymetry in the shallow water regime. It is an asymp…
Local well-posedness result for a class of non-local quasi-linear systems and its application to the justification of Whitham-Boussinesq systems
Louis Emerald
In this paper we prove a local well-posedness result for a class of quasi-linear systems of hyperbolic type involving Fourier multipliers. Among the physically relevant systems in…
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…
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…