4 papers
Dissipative solutions to randomly forced 3D Euler equations
Umberto Pappalettera, Francesco Triggiano
The purpose of this work is twofold. First, we construct probabilistically strong solutions to the three-dimensional Euler equations perturbed by additive noise that are $\mathbb{P…
Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion
Eliseo Luongo, Francesco Triggiano
We study a slow-fast system of coupled two- and three-dimensional Navier-Stokes equations in which the fast component is perturbed by an additive fractional Brownian noise with Hur…
Effective continuous equations for adaptive SGD: a stochastic analysis view
Luca Callisti, Marco Romito, Francesco Triggiano
We present a theoretical analysis of some popular adaptive Stochastic Gradient Descent (SGD) methods in the small learning rate regime. Using the stochastic modified equations fram…
Non-uniqueness of weak solutions for a logarithmically supercritical hyperdissipative Navier-Stokes system
Marco Romito, Francesco Triggiano
The existence of non-unique solutions of finite kinetic energy for the three dimensional Navier-Stokes equations is proved in the slightly supercritical hyper-dissipative setting i…