4 papers
Optimal mixing and enhanced dissipation for a smooth velocity field in any spatial dimension
Luca Melzi
In this note, we consider the advection-diffusion equation on the -dimensional torus, where is arbitrary. First, for the associated transport equation, we provide an explici…
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…
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…
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…