7 papers
The shallow--water limit of linear water waves over a discontinuous bottom
Martin Oen Paulsen
We rigorously justify the zero--dispersion limit of linear water waves over a sharp bottom step, recovering the shallow-water equations as a transmission problem, and describe the…
The F. John model and Cummins' equations for freely floating objects
David Lannes, Martin Oen Paulsen
In this paper, we address the well-posedness theory of F. John's problem for freely floating objects in a two-dimensional framework. This problem is a linear description of the int…
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…
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…
Long time well-posedness of Whitham-Boussinesq systems
Martin Oen Paulsen
Consideration is given to three different full dispersion Boussinesq systems arising as asymptotic models in the bi-directional propagation of weakly nonlinear surface waves in sha…
A Nonlinear Formulation of Radiation Stress and Applications to Cnoidal Shoaling
Martin O. Paulsen, Henrik Kalisch
In this article we provide formulations of energy flux and radiation stress consistent with the scaling regime of the Korteweg-de Vries (KdV) equation. These quantities can be used…