Blar i Bergen Open Research Archive på forfatter "Paulsen, Martin Oen"
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Admissibility conditions for Riemann data in shallow water theory
Paulsen, Martin Oen; Kalisch, Henrik (Journal article; Peer reviewed, 2020)Consideration is given to the shallow-water equations, a hyperbolic system modeling the propagation of long waves at the surface of an incompressible inviscible fluid of constant depth. It is well known that the solution ... -
Justification of the Benjamin–Ono equation as an internal water waves model
Paulsen, Martin Oen (Journal article; Peer reviewed, 2024)In this paper, we give the first rigorous justification of the Benjamin-Ono equation: $$\begin{aligned} \hspace{3cm} \partial _t \zeta + (1 - \frac{\gamma }{2}\sqrt{\mu }|\textrm{D}|)\partial _x \zeta + \frac{3{\varepsilon ... -
Long time well-posedness and full justification of a Whitham-Green-Naghdi system
Emerald, Louis; Paulsen, Martin Oen (Journal article; Peer reviewed, 2024)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 asymptotic model of the water waves equations ... -
Long time well-posedness of Whitham-Boussinesq systems
Paulsen, Martin Oen (Journal article; Peer reviewed, 2022)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 shallow water. We prove that, under a ... -
A Nonlinear Formulation of Radiation Stress and Applications to Cnoidal Shoaling
Paulsen, Martin Oen; Kalisch, Henrik (Journal article; Peer reviewed, 2021)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 to describe the shoaling of cnoidal waves ... -
On the relation between wave conditions and mathematical properties of some asymptotic water wave models
Paulsen, Martin Oen (Master thesis, 2020-06-06) -
Rigorous derivation of some asymptotic models for free water surfaces and interfaces
Paulsen, Martin Oen (Doctoral thesis, 2024-04-26)Opprinnelsen til moderne matematisk hydrodynamikk kan spores tilbake til 1700-tallet. I 1757 publiserte Euler artikkelen der han introduserte ligninger, i dag kjent som Euler likningene, som kan beskrive væskedynamikk [31]. ... -
Rigorous derivation of weakly dispersive shallow-water models with large amplitude topography variations
Emerald, Louis; Paulsen, Martin Oen (Journal article; Peer reviewed, 2024)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 dimensions one and two. The systems are made to ...