School of Mathematical Physics

The Summer School of Mathematical Physics of the National Group of Mathematical Physics took place September 1-11 2026 in Ravello. I gave five lectures on the modelling of surface and internal waves.

1. General ideas on asymptotic modelling. Motivation on why modelling is crucial, and why rigorous asymptotic modelling matters.
2. Rigorous justification of the shallow-water system, starting from the water-waves system. A peek on refined, higher-order models.
3. Singular limits in general, and application to the relaxed (or “hyperbolized”) Green-Naghdi system.
4. Introduction to internal waves. Questions of well-posedness/ill-posedness and spectral stability, depending on shear velocity and stratification.
5. Introduction to interfacial waves. Kelvin-Helmholtz instability, and the limit of sharp stratification.

The slides of the lecture notes are available here.

An associated Jupyter notebook is available here. It can be viewed on this url, and interacted with on your laptop provided you installed Julia language.