33 citations · 88 across the 16 of their papers we have counts for
17 papers
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 initial data and driven by a spatially roug…
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-…
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 Hölder regular in space (rough Kraichnan's model), a well established sy…
Almost-everywhere uniqueness of Lagrangian trajectories for D Navier--Stokes revisited
Lucio Galeati
We show that, for any Leray solution to the D Navier--Stokes equations with , the associated deterministic and stochastic Lagrangian trajectories are unique for…
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 with parameter , an active scalar model interpolating between SQG () and th…
Quantitative Propagation of Chaos for Singular Interacting Particle Systems Driven by Fractional Brownian Motion
Lucio Galeati, Khoa Lê, 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…
Weak well-posedness by transport noise for a class of 2D fluid dynamics equations
Lucio Galeati, Dejun Luo
A fundamental open problem in fluid dynamics is whether solutions to D Euler equations with -valued vorticity are unique, for some . A relate…
LDP and CLT for SPDEs with Transport Noise
Lucio Galeati, Dejun Luo
In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the c…
Distribution dependent SDEs driven by additive fractional Brownian motion
Lucio Galeati, Fabian A. Harang, Avi Mayorcas
We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter…
Distribution dependent SDEs driven by additive continuous noise
Lucio Galeati, Fabian A. Harang, Avi Mayorcas
We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [16]. We…
Eddy heat exchange at the boundary under white noise turbulence
Franco Flandoli, Lucio Galeati, Dejun Luo
We prove the existence of an eddy heat diffusion coefficient coming from an idealized model of turbulent fluid. A difficulty lies in the presence of a boundary, with also turbulent…
Quantitative convergence rates for scaling limit of SPDEs with transport noise
Franco Flandoli, Lucio Galeati, Dejun Luo
We consider on the torus the scaling limit of stochastic 2D (inviscid) fluid dynamical equations with transport noise to deterministic viscous equations. Quantitative estimates on…
Nonlinear Young differential equations: a review
Lucio Galeati
Nonlinear Young integrals have been first introduced in [Catellier,Gubinelli, SPA 2016] and provide a natural generalisation of classical Young ones, but also a versatile tool in t…
Delayed blow-up by transport noise
Franco Flandoli, Lucio Galeati, Dejun Luo
For some deterministic nonlinear PDEs on the torus whose solutions may blow up in finite time, we show that, under suitable conditions on the nonlinear term, the blow-up is delayed…
Regularization of multiplicative SDEs through additive noise
Lucio Galeati, Fabian A. Harang
We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz require…
Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier-Stokes equations
Franco Flandoli, Lucio Galeati, Dejun Luo
We consider a family of stochastic 2D Euler equations in vorticity form on the torus, with transport type noises and -initial data. Under a suitable scaling of the noises, we…
On the convergence of stochastic transport equations to a deterministic parabolic one
Lucio Galeati
A stochastic transport linear equation (STLE) with multiplicative space-time dependent noise is studied. It is shown that, under suitable assumptions on the noise, a multiplicative…