Lucio Galeati

activity

20242026

collaborators

7 papers

math.PR2026

Anomalous Regularization in Kraichnan's Passive Scalar Model

Lucio Galeati, Francesco Grotto, Mario Maurelli

We consider the advection of a passive scalar by a divergence free random Gaussian field, white in time and HÃ¶lder regular in space (rough Kraichnan's model), a well established s…

math.PR2026

Refined uniqueness results for 2D Euler and gSQG with rough Kraichnan noise

Marco Bagnara, Lucio Galeati

We prove strong well-posedness results for the stochastic 2D Euler equations in vorticity form and generalized SQG equations, with $L^{p}$ initial data and driven by a spatially roug…

math.PR2025

Quantitative Propagation of Chaos for Singular Interacting Particle Systems Driven by Fractional Brownian Motion

Lucio Galeati, Khoa LÃª, Avi Mayorcas

We consider interacting systems particle driven by i.i.d. fractional Brownian motions, subject to irregular, possibly distributional, pairwise interactions. We show propagation of…

math.PR2025

Regularization by rough Kraichnan noise for the generalised SQG equations

Marco Bagnara, Lucio Galeati, Mario Maurelli

We consider the generalised Surface Quasi-Geostrophic (gSQG) equations in $R^{2}$ with parameter $I^^{2} \in (0, 1)$ , an active scalar model interpolating between SQG ( $I^^{2} = 1$ ) and…

math.AP2025

Almost-everywhere uniqueness of Lagrangian trajectories for $3$ D Navier--Stokes revisited

Lucio Galeati

We show that, for any Leray solution $u$ to the $3$ D Navier--Stokes equations with $u_{0} \in L^{2}$ , the associated deterministic and stochastic Lagrangian trajectories are unique for…

math.AP2025

On the well-posedness of (nonlinear) rough continuity equations

Lucio Galeati, James-Michael Leahy, Torstein Nilssen

Motivated by applications to fluid dynamics, we study rough differential equations (RDEs) and rough partial differential equations (RPDEs) with non-Lipschitz drifts. We prove well-…