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math.AP2023
Justification of the Benjamin-Ono equation as an internal water waves model
Martin Oen Paulsen
In this paper, we give the first rigorous justification of the Benjamin-Ono equation as an internal water wave model on the physical time scale. Let be the small para…
math.AP2023
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…
math.AP2023
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…