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Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems
We rigorously justify the bilayer shallow-water system as an approximation to the hydrostatic Euler equations in situations where the …
Mahieddine Adim, Roberta Bianchini, Vincent Duchêne
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On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity
This article is concerned with rigorously justifying the hydrostatic limit for continuously stratified incompressible fluids under the …
Roberta Bianchini, Vincent Duchêne
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Rectification of a deep water model for surface gravity waves
In this work we discuss an approximate model for the propagation of deep irrotational water waves, specifically the model obtained by …
Vincent Duchêne, Benjamin Melinand
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A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part II
We consider the Kakinuma model for the motion of interfacial gravity waves. The Kakinuma model is a system of Euler-Lagrange equations …
Vincent Duchêne, Tatsuo Iguchi
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A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part I.
We consider a model, which we named the Kakinuma model, for interfacial gravity waves. As is well-known, the full model for interfacial …
Vincent Duchêne, Tatsuo Iguchi
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Stability and instability in scalar balance laws: fronts and periodic waves
We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and …
Vincent Duchêne, L. Miguel Rodrigues
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Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart
We perform numerical experiments on the Serre-Green-Naghdi (SGN) equations and a fully dispersive “Whitham-Green-Naghdi” …
Vincent Duchêne, Christian Klein
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Large-time asymptotic stability of Riemann shocks of scalar balance laws
We prove the large-time asymptotic orbital stability of strictly entropic Riemann shock solutions of first-order scalar hyperbolic …
Vincent Duchêne, L. Miguel Rodrigues
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A Hamiltonian structure of the Isobe–Kakinuma model for water waves
We consider the Isobe–Kakinuma model for water waves, which is obtained as the system of Euler–Lagrange equations for a Lagrangian …
Vincent Duchêne, Tatsuo Iguchi
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Rigorous justification of the Favrie–Gavrilyuk approximation to the Serre–Green–Naghdi model
The (Serre–)Green–Naghdi system is a non-hydrostatic model for the propagation of surface gravity waves in the shallow-water regime. …
Vincent Duchêne
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