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20232026
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math.AP2026

Long time strong Sobolev instability for quasilinear NLS

Yuri Cacchiò, Filippo Giuliani, Felice Iandoli +1

We prove long-time strong Sobolev instability for a class of quasilinear Schrödinger equations on arising, via the Madelung transform, in the description of Euler-Kor…

math.AP2026

Local Bifurcations from Single-Mode Traveling Waves in the Filamentation Equation

Yuri Cacchiò

We study local bifurcations from the single-mode traveling wave family of the filamentation equation on the torus, within the real positive-frequency Sobolev space . A Fourier…

math.AP2026

Formal Stability of Tetrahedral Non-Zonal Flows on the Sphere

Yuri Cacchiò

We investigate the formal stability of finite-amplitude non-zonal flows bifurcating from the trivial state in the unforced 2D Euler equations on the sphere. To bypass the degenerac…

math.AP2026

Bifurcation of Tetrahedral Non-Zonal Flows in the 2D Euler Equations on a Rotating Sphere

Yuri Cacchiò

We investigate the emergence of finite-amplitude non-zonal flows on the sphere arising from stationary solutions to the 2D Euler equations. By restricting the Laplac…

math.AP2025

The zero capillarity limit for the Euler-Korteweg system with no-flux boundary conditions

Paolo Antonelli, Yuri Cacchiò

In this article, we study the small dispersion limit of the Euler-Korteweg system in a domain with a smooth boundary and no-flux boundary conditions. We exploit a relative energy a…

math.AP2025

On the effect of the Coriolis force on the enstrophy cascade

Yuri Cacchiò, Amirali Hannani, Gigliola Staffilani

We study the direct enstrophy cascade at small spatial scales in statistically stationary forced-dissipated 2D Navier-Stokes equations subject to the Coriolis force in the -plan…

math.AP2023

Well-Posedness and regularity properties of 2d -plane stochastic Navier-Stokes equations in a periodic channel

Yuri Cacchio', Amirali Hannani, Gigliola Staffilani

We consider the 2d -plane stochastic Navier-Stokes equations in a periodic channel. We prove the well-posedness and existence of the stationary measure, as well as certain regul…

math.AP2023

Global Well-Posedness for Eddy-Mean Vorticity Equations on

Yuri Cacchió

We consider the two-dimensional, -plane, vorticity equations for an incompressible flow, where the zonally averaged flow varies on scales much larger than the perturbation. We p…