GUnDHam

Project 101124921

ERC - COG - 2023

Generating Unstable Dynamics in dispersive Hamiltonian fluids

GUnDHam is funded by the ERC Consolidator grant call 2023, receiving a budget of about 1.500.000 Euros.

This project aims to prove rigorous results on the generation of unstable dynamics in the dispersive Hamiltonian water waves and geophysical fluid equations: for example formation of energy cascades from low to high frequencies, orbital instabilities and extreme rare phenomena such as rogue waves. All these behaviors are well documented in experiments, real world data and numerical simulations, but still lack a rigorous mathematical proof. Accordingly the project has three lines of research:

Energy cascades from low to high frequency modes
Modulational and orbital instabilities of traveling waves
Extreme phenomena formations

Team members

Alberto Maspero

Alberto is the PI of the project. He is associate Professor at SISSA since 2022. Previously, he has been assistant Professor at SISSA. He got a PhD in Mathematics in 2014, in cotutelle between the University of Zurich and University of Milan. He is a mathematician who works on Partial Differential Equations (PDEs) and infinite dimensional Hamiltonian systems.

Shulamit Terracina

Shulamit is the first postdoc to join GUnDHam! She will very soon complete her PhD at University of Milan, Italy. Her expertise is the construction of quasi-periodic solutions for quasi-linear PDEs arising from fluids via KAM methods. In GUnDHam, she will work on problems regarding energy cascades from low to high frequencies in quasi-linear equations.

Projects

Energy cascades

One of the most important problem in physics, mathematical analysis and engineering is to study how energy is transferred and redistributed from macro to micro scales in a deterministic system. This question is central to understand the insurgence of turbulent dynamics. In fluids, it is characterized by a nonlinear transfer of energy from low to high Fourier modes, in a process called cascade, which is the result of non-linear resonant interactions between different wave components. The goal of this project is to study cascades formation in dispersive Hamiltonian fluids.

Modulational instability

Modulational instability is the ubiquitous phenomenon in physics of a traveling wave being unstable under small amplitude long-wave perturbations. The goal of this project is to prove linear and nonlinear modulational instability of space periodic traveling wave solutions in water waves and geophysical fluids, such as Stokes and Rossby waves.

Rogue waves formation

Rogue waves are extreme phenomena in which waves of extreme height appear suddenly in open waters. Once considered figments of imagination of sailors, they are today recognized as a serious threat to ships and sea structures. We plan to construct rogue wave solutions of the water wave equations, confirming (or disproving) two of the most renowned physical conjectures regarding their formation. This will be achieved combining deterministic normal forms and probabilistic methods, like large deviation principles applied to PDEs.

Host institution

SISSA – Scuola Internazionale Superiore di Studi Avanzati – was founded in 1978 and is a scientific center of excellence within the national and international academic scene.

Located in Italy, in the city of Trieste, it features about 70 professors, 130 researchers, 300 PhD students. The School is surrounded by a 25 acre park, and offers a stunning view of the Gulf of Trieste. The quality level of the research is further confirmed by the fact that within the competitive field of European funding schemes SISSA holds the top position among Italian scientific institutes in terms of research grants obtained in relation to the number of researchers and professors.

Publications

T. Barbieri, M. Berti, A. Maspero, M. Mazzuchelli (2025). Bifurcation of gravity-capillary Stokes waves with constant vorticity.

PDF Code Project arXiv

M. Berti, A. Maspero, P. Ventura (2025). First isola of modulational instability of Stokes waves in deep water.

PDF Code Project EMS Surv. Math. Sci

M. Berti, L. Corsi, A. Maspero, P. Ventura (2025). On higher order isolas of unstable Stokes waves.

PDF Code Project arXiv

B. Langella, A. Maspero, M.T. Rotolo (2024). Growth of Sobolev norms for completely resonant quantum harmonic oscillators on R^2.

PDF Project Poster Video arXiv

A. Maspero, F. Murgante (2024). One dimensional energy cascades for a fractional quasilinear NLS.

PDF Dataset Project Poster Video Source Document arXiv

Open access policy

All papers published under ERC grants must comply with a specific open access policy. This is a quick recap of best practices for compliance, meant for project members:

Put all preprints on a public repository before submission (arXiv, HAL, SISSA preprint server). Note that CVGMT does not qualify as an open access repository.
Before submission, check the policy of the journal. It must permit the publication of the accepted version of the paper on a public repository with an embargo period not longer than 6 months. Use the following tool: Open Policy Finder.
After acceptance, update the preprint server with the accepted version as soon as the embargo period has elapsed. Provide the DOI link as soon as it is available.
An alternative to the previous two points applies to journals that have special agreements with the HI and allow for gold open access publication without fees.

A list of such agreements is available here: Read & Publish Transformative Agreements.

Official guidelines can be found here: ERC Open Access Guidelines.

Contact

We always look for new potential members or collaborations, feel free to contact us

gundham.erc@proton.me
Via Bonomea 265, Trieste, 34126