Related papers: Stochastic inviscid shell models: well-posedness a…
Shell models provide a simplified mathematical framework that captures essential features of incompressible fluid turbulence, such as the energy cascade and scaling of the fluid observables. We perform a precision analysis of the direct and…
In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…
A spherical shell model for turbulence, obtained by coupling $N$ replicas of the Gledzer, Okhitani and Yamada shell model, is considered. Conservation of energy and of an helicity-like invariant is imposed in the inviscid limit. In the $N…
Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…
The GOY model is a model for turbulence in which two conserved quantities cascade up and down a linear array of shells. When the viscosity parameter, $\nu$, is small the model has a qualitative behavior which is similar to the Kolmogorov…
The application of machine learning (ML) techniques, especially neural networks, has seen tremendous success at processing images and language. This is because we often lack formal models to understand visual and audio input, so here neural…
The three-dimensional inviscid Hasegawa-Mima model is one of the fundamental models that describe plasma turbulence. The model also appears as a simplified reduced Rayleigh-B\'enard convection model. The mathematical analysis the…
Modeling the intermittent behavior of turbulent energy dissipation processes both in space and time is often a relevant problem when dealing with phenomena occurring in high Reynolds number flows, especially in astrophysical and space…
We deal with a class of abstract nonlinear stochastic models, which covers many 2D hydrodynamical models including 2D Navier-Stokes equations, 2D MHD models and 2D magnetic B\'enard problem and also some shell models of turbulence. We first…
An earlier paper presented the potentially significant discovery that disturbances in simplified simulations of a stellar disc model that was predicted to be stable in linear theory grew to large amplitude over a long period of time. The…
The inviscid 2D Boussinesq system with thermal diffusivity and multiplicative noise of transport type is studied in the $L^2$-setting. It is shown that, under a suitable scaling of the noise, weak solutions to the stochastic 2D Boussinesq…
Instabilities of fluid flows often generate turbulence. Using extensive direct numerical simulations, we study two-dimensional turbulence driven by a wavenumber-localised instability superposed on stochastic forcing, in contrast to previous…
We introduce a class of multi-scale systems with discrete time, motivated by the problem of inviscid limit in fluid dynamics in the presence of small-scale noise. These systems are infinite-dimensional and defined on a scale-invariant…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
We introduce a model for the turbulent energy cascade aimed at studying the effect of dynamical scaling on intermittency. In particular, we show that by slowing down the energy transfer mechanism for fixed energy flux, intermittency…
We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions and we show that…
In this paper, we study the well-posedness properties of a stochastic rotating shallow water system in which the noise is chosen according to the Stochastic Advection by Lie Transport (SALT) theory. The system is perturbed by noise…
In this paper, we prove the global existence of strong solutions for the 3D incompressible inhomogeneous viscoelastic system. We do not assume the "initial state" assumption and the "div-curl" structure inspired by the works [59,61]. It is…
We consider a model for an incompressible visoelastic fluid. It consists of the Navier-Stokes equations involving an elastic term in the stress tensor and a transport equation for the evolution of the deformation gradient. The novel feature…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…