Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method under the moderated interaction…
A broad class of possibly non-unique generalized kinetic solutions to hyperbolic-parabolic PDEs is introduced. Optimal regularity estimates in time and space for such solutions to nonlocal, and spatially inhomogeneous variants of the porous medium equation are shown in the scale of Sobolev…
Accepted / forthcoming · Annals of Applied Probability. The dynamical large deviations principle for the three-dimensional incompressible Landau-Lifschitz-Navier-Stokes equations is shown, in the joint scaling regime of vanishing noise intensity and correlation length. This proves the consistency of the large…
Published · Mathematical Methods in the Applied Sciences 47(11), 9222–9248 (2024). The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence argument to treat…
Published · Stochastic PDE: Analysis and Computations 13, 1502–1557 (2025). Recently, many existence results for the stochastic thin-film equation were established in the case of a quadratic mobility exponent $n=2$, in which the noise term $\partial_x(u^\frac{n}{2}\mathcal{W})$ becomes linear. In the case of…
Published · Journal of Dynamics and Differential Equations 37, 1997–2001 (2025). In the article ‘Criteria for Strong and Weak Random Attractors’ necessary and sufficient conditions for strong attractors and weak attractors are studied. In this note we correct two of its theorems on…
Published · Milan Journal of Mathematics 92(2), 397–425 (2024). We consider an inviscid 3-layer quasi-geostrophic model with stochastic forcing in a 2D bounded domain. After establishing well-posedness of such system under natural regularity assumptions on the initial condition and the (additive) noise, we prove the existence of an invariant…
Published · Annals of Applied Probability (2024). We consider a system of N point vortices in a bounded domain with null total circulation, whose statistics are given by the Canonical Gibbs Ensemble at inverse temperature $\beta\geq 0$. We prove…
Published · Mathematische Annalen 390(2), 2727–2766 (2024). The paper is devoted to the analysis of the global well-posedness and the interior regularity of the 2D Navier-Stokes equations with inhomogeneous stochastic boundary conditions. The noise, white in time and coloured…
Book · Springer, Lecture Notes in Mathematics 2330 (2023). Franco Flandoli and Eliseo Luongo introduce stochastic Navier–Stokes equations, transport noise and turbulence modelling.
Published · Electronic Journal of Probability 29, 1–42 (2024). Using a weak convergence approach, we establish a Large Deviation Principle (LDP) for the solutions of fluid dynamic systems in two-dimensional bounded domains subjected to no-slip boundary conditions and perturbed by additive noise. Our analysis considers the convergence of both…
Published · Transactions of the American Mathematical Society, 379 (2026) 4, pp. 2343-2383. The stochastic thin-film equation with mobility exponent $n\in [\frac{8}{3},3)$ on the one-dimensional torus with multiplicative Stratonovich noise is considered. We show that martingale solutions exist for non-negative initial values. This advances on…
