413 citations · 1.5k across the 79 of their papers we have counts for
64 papers · 1 filter
Stochastic transport by Gaussian noise
Franco Flandoli, Francesco Russo
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is th…
On the Boussinesq hypothesis for a stochastic Proudman-Taylor model
Franco Flandoli, Dejun Luo
We introduce a stochastic version of Proudman-Taylor model, a 2D-3C fluid approximation of the 3D Navier-Stokes equations, with the small-scale turbulence modeled by a transport-st…
2D Smagorinsky type large eddy models as limits of stochastic PDEs
Franco Flandoli, Dejun Luo, Eliseo Luongo
We prove that a version of Smagorinsky Large Eddy model for a 2D fluid in vorticity form is the scaling limit of suitable stochastic models for large scales, where the influence of…
Noise based on vortex structures in 2D and 3D
Franco Flandoli, Ruojun Huang
A new noise, based on vortex structures in 2D (point vortices) and 3D (vortex filaments), is introduced. It is defined as the scaling limit of a jump process which explores vortex…
Coagulation dynamics under environmental noise: scaling limit to SPDE
Franco Flandoli, Ruojun Huang
We prove that a system of locally interacting diffusions carrying discrete masses, subject to an environmental noise and undergoing mass coagulation, converges to a system of Stoch…
From additive to transport noise in 2D fluid dynamics
Franco Flandoli, Umberto Pappalettera
Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multisca…
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…
Mean field limit of point vortices with environmental noises to deterministic 2D Navier-Stokes equations
Franco Flandoli, Dejun Luo
We consider point vortex systems on the two dimensional torus perturbed by environmental noise. It is shown that, under a suitable scaling of the noises, weak limit points of the e…
2D Euler equations with Stratonovich transport noise as a large scale stochastic model reduction
Franco Flandoli, Umberto Pappalettera
The limit from an Euler type system to the 2D Euler equations with Stratonovich transport noise is investigated. A weak convergence result for the vorticity field and a strong conv…
The KPP equation as a scaling limit of locally interacting Brownian particles
Franco Flandoli, Ruojun Huang
Fisher-KPP equation is proved to be the scaling limit of a system of Brownian particles with local interaction. Particles proliferate and die depending on the local concentration o…
An Example of Intrinsic Randomness in Deterministic PDEs
Franco Flandoli, Benjamin Gess, Francesco Grotto
A new mechanism leading to a random version of Burgers' equation is introduced: it is shown that the Totally Asymmetric Exclusion Process in discrete time (TASEP) can be understood…
Stochastic model reduction: convergence and applications to climate equations
Sigurd Assing, Franco Flandoli, Umberto Pappalettera
We study stochastic model reduction for evolution equations in infinite dimensional Hilbert spaces, and show the convergence to the reduced equations via abstract results of Wong-Z…
Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation
Franco Flandoli, Dejun Luo, Cristiano Ricci
Stochastic Differential Equations (SDEs) in high dimension, having the structure of finite dimensional approximation of Stochastic Partial Differential Equations (SPDEs), are consi…
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…
Epidemic Models as Scaling Limits of Individual Dynamics
Franco Flandoli, Francesco Grotto, Andrea Papini +1
Infection spread among individuals is modelled with a continuous time Markov chain, in which subject interactions depend on their distance in space. The well known SIR model and no…
On the relation between the Girsanov transform and the Kolmogorov equations for SPDEs
Franco Flandoli, Dejun Luo, Cristiano Ricci
The Girsanov transform and Kolmogorov equations are two useful methods for studying SPDEs. It is shown that, under suitable conditions, the series expansion obtained from the Girsa…
On the Macroscopic limit of Brownian Particles with local interaction
Franco Flandoli, Marta Leocata, Cristiano Ricci
An interacting particle system made of diffusion processes with local interaction is considered and the macroscopic limit to a nonlinear PDE is investigated. Few rigorous results e…
Global well-posedness of the 3D Navier--Stokes equations perturbed by a deterministic vector field
Franco Flandoli, Martina Hofmanová, Dejun Luo +1
We are concerned with the problem of global well-posedness of the 3D Navier--Stokes equations on the torus with unitary viscosity. While a full answer to this question seems to be…
Uniform approximation of 2 Navier-Stokes equation by stochastic interacting particle systems
Franco Flandoli, Christian Olivera, Marielle Simon
We consider an interacting particle system modeled as a system of stochastic differential equations driven by Brownian motions. We prove that the (mollified) empirical process…
Stochastic Navier-Stokes Equations and Related Models
Luigi Amedeo Bianchi, Franco Flandoli
Regularization by noise for certain classes of fluid dynamic equations, a theme dear to Giuseppe Da Prato (see G. Da Prato and A. Debussche, Ergodicity for the 3D stochastic Navier…
High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations
Franco Flandoli, Dejun Luo
The paper is devoted to the open problem of regularization by noise of 3D Navier-Stokes equations. Opposite to several attempts made with additive noise which remained inconclusive…
A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis
Franco Flandoli, Dejun Luo, Cristiano Ricci
For Kolmogorov equations associated to finite dimensional stochastic differential equations (SDEs) in high dimension, a numerical method alternative to Monte Carlo simulations is p…
Fokker-Planck equation for dissipative 2D Euler equations with cylindrical noise
Franco Flandoli, Francesco Grotto, Dejun Luo
After a short review of recent progresses in 2D Euler equations with random initial conditions and noise, some of the recent results are improved by exploiting a priori estimates o…
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…