Research

The research activity of the group is supported by:

• EU-HORIZON EUROPE ERC-2021-ADG  “Noise in Fluids” (NoisyFluid), no. 101053472

• PRIN "Noise in fluid dynamics and related models", 20222YRYSP

• PRIN-PNRR "Some mathematical approaches to climate change and its impacts", P20225SP98

• MUR_PRO3_2021-23 “Teorie e strumenti per la transizione ecologica: profili filosofici, etici e giuridici relativi alle sfide di sostenibilità del carbon budget”

In different forms, these projects are linked to Stochastic fluid dynamics, a topic at the interface between Probability, PDE theory, mathematical physics and geophysics, with inputs from dynamical systems and computational sciences. 

It deals with fluid dynamic models, usually described by PDEs but sometimes also by particle systems, perturbed by noise. 

Our main focuses are physically motivated noise inputs and the consequences they have. A major role is played by the description by noise of turbulence, like stochastic models of small turbulent scales and the corresponding forms of stochastic PDEs that arise.

Our investigation of the consequences of noise in fluids range from theoretical consequences of interest for the mathematical foundations to consequences of interest for physics and applications.

A key foundational question is regularisation by noise, namely the possibility that a particular noise source improves the results of the deterministic theory. We are also interested in the links with other theories like those of non uniqueness and exotic solutions and the concepts of intrinsic stochasticity.

Among the properties of physical interest we deal with enhanced viscosity and diffusion provoked by turbulence, enhanced coalescence of particles, the effect of turbulence on vector fields, like the dynamo effect, and on polymers and nonNewtonian fluids, the link between turbulence and zonal flows, as well as the impact on geophysical dynamics and climate.