3 papers
math.AP2026
Arnold stability and rigidity in Zeitlin's model of hydrodynamics
Luca Melzi, Klas Modin
Zeitlin's model is a discretisation of the 2-D Euler equations that preserves the underlying geometric structure. This feature makes it suitable for studying the qualitative behavi…
math.AP2025
Quantitative stability of the Rossby--Haurwitz waves of degree two for the Euler equation on
Matias G. Delgadino, Luca Melzi
We show that the degree-2 Rossby--Haurwitz travelling waves on the Euler equation on are orbitally stable. Our proof is short, quantitative, and conceptually easy to…
math.AP2025
On a non-local phase-field model for tumour growth with single-well Lennard-Jones potential
Maurizio Grasselli, Luca Melzi, Andrea Signori
In the present work, we develop a comprehensive and rigorous analytical framework for a non-local phase-field model that describes tumour growth dynamics. The model is derived by c…