
Eliseo Luongo

Dr. · Postdoctoral Researcher
TU Berlin
Research profile
Eliseo Luongo works on stochastic partial differential equations and nonlinear PDEs, with a particular focus on problems arising in fluid mechanics and transport theory. A central theme of his research is understanding the mechanisms governing well-posedness and non-uniqueness in these equations. He studies how stochastic perturbations can regularize the dynamics, enhance dissipation, or select solutions in singular regimes, as well as how instability mechanisms can lead to non-uniqueness in supercritical PDEs.
Research areas
SPDEs · Fluid Dynamics · Regularization by Noise · Instability and Non-Uniqueness
Five research keywords
stochastic fluid dynamics · transport noise · Navier–Stokes equations · scaling limits · supercritical PDEs
Contact and links
Academic links
Curriculum vitae
| Date | Appointment / education |
|---|---|
| Current | Postdoctoral researcher, Stochastic Analysis in the Sciences, Technische Universität Berlin. |
| September 2024–September 2026 | Postdoctoral researcher, Bielefeld University. |
| November 2020–September 2024 | PhD, Scuola Normale Superiore, Pisa, supervised by Prof. Franco Flandoli. Thesis: Stochastic Problems for Turbulent Fluids in Domains with Boundaries. |
| October 2020 | Degree in Mathematical Engineering, Politecnico di Milano. |
Publications
This catalogue contains all publications by the member, including work from before joining SAiS. Journal versions and preprints are maintained as one record per scientific work.
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Background Vlasov equations and Young measures for passive scalar and vector advection equations under special stochastic scaling limits
Published · Probability Theory and Related Fields (2026). In the last few years it was proved that scalar passive quantities subject to suitable stochastic transport noise, and more recently that also vector passive quantities subject to suitable stochastic transport and…
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Global well-posedness of 2D Navier-Stokes with Dirichlet boundary fractional noise
Published · Nonlinearity 38, 075023 (2025). In this paper, we prove the global well-posedness and interior regularity for the 2D Navier-Stokes equations driven by a fractional noise acting as an inhomogeneous Dirichlet-type boundary condition. The model describes a…
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Mean-Field Magnetohydrodynamics Models as Scaling Limits of Stochastic Induction Equations
We study the asymptotic properties of a stochastic model for the induction equations of the magnetic field in a three dimensional periodic domain. The turbulent velocity field driving the electromotive force on the magnetic field is modeled by a noise…
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On the Itô-Stratonovich Diffusion Limit for the Magnetic Field in a 3D Thin Domain
Published · Stochastics and Partial Differential Equations: Analysis and Computations (2026). We introduce a stochastic model for a passive magnetic field in a three dimensional thin domain. The velocity field, white in time and modelling phenomenologically a turbulent fluid, acts on the magnetic field as a transport-stretching noise. We prove, in…
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Existence of Invariant Measures for Stochastic Inviscid Multi-Layer Quasi-Geostrophic Equations
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…
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Gibbs Equilibrium Fluctuations of Point Vortex Dynamics
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…
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Global well-Posedness and Interior Regularity of 2D Navier-Stokes Equations with Stochastic Boundary Conditions
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…
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Stochastic Partial Differential Equations in Fluid Mechanics
Book · Springer, Lecture Notes in Mathematics 2330 (2023). Franco Flandoli and Eliseo Luongo introduce stochastic Navier–Stokes equations, transport noise and turbulence modelling.
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Large Deviations Principle for the Inviscid Limit of Fluid Dynamic Systems in 2D Bounded Domains
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…
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2D Smagorinsky type large eddy models as limits of stochastic PDEs
Published · Journal of Nonlinear Science 34, 54 (2024). 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…
Current SAiS projects
No current SAiS project assignment has been confirmed; information should be provided if applicable.
Talks and posters
Talks
| Date | Talk |
|---|---|
| September 2026 | Spectral instability in fluid mechanics and non-uniqueness for the Keller-Segel system, Conference on Deterministic and SPDEs in Fluid Dynamics and Beyond, York, United Kingdom. |
| September 2026 | Anomalous Regularization and Dissipation for 2D Euler Equations with Rough Kraichnan Noise, DMV Annual Meeting, Konstanz, Germany. |
| July 2026 | Anomalous Regularization and Dissipation for 2D Euler Equations with Rough Kraichnan Noise, 15th AIMS Conference, Athens, Greece. |
| June 2026 | Anomalous Regularization and Dissipation for 2D Euler Equations with Rough Kraichnan Noise, Fifth Italian Meeting of Probability and Mathematical Statistics, Palermo, Italy. |
| September 2025 | Zero-noise Selection for the Stochastic Transport Equation beyond DiPerna–Lions, Mathematical Analysis of Fluid Flows by Variational Methods, Berlin, Germany. |
| July 2025 | Spectral instability in fluid mechanics and non-uniqueness of supercritical heat equations, Analysis Seminar, Basel, Switzerland. |
| December 2024 | Mean-Field Magnetohydrodynamics Models as Scaling Limits of Stochastic Induction Equations, M.A.P. Seminars, Pisa, Italy. |
| June 2024 | Global Well-Posedness and Interior Regularity of 2D Navier–Stokes Equations with Stochastic Wind Driven Boundary Conditions, Fourth Italian Meeting of Probability and Mathematical Statistics, Rome, Italy. |
| May 2024 | Global Well-Posedness and Interior Regularity of 2D Navier–Stokes Equations with Stochastic Wind Driven Boundary Conditions, SPDEvent, Bielefeld, Germany. |
| April 2024 | Global Well-Posedness and Interior Regularity of 2D Navier–Stokes Equations with Stochastic Wind Driven Boundary Conditions, Polimi Probability Seminars, Politecnico di Milano, Milan, Italy. |
| January 2024 | A Stochastic Particle Approximation of the 2D Navier–Stokes Equations with Vorticity Generation, Seminars in Analysis and Applications, TU Delft, Netherlands. |
| July 2023 | A Stochastic Particle Approximation Approach of the 2D Navier–Stokes Equations with Vorticity Generation, 43rd Conference on Stochastic Processes and their Applications, Lisbon, Portugal. |
| January 2023 | A Stochastic Particle Approximation Approach of the 2D Navier–Stokes Equations with Vorticity Generation, PMS² Pavia–Milano Seminar Series on Probability and Mathematical Statistics, Milan, Italy. |
| October 2022 | Inviscid Limit for Stochastic Second-Grade Fluid Equations, Oberwolfach Seminar: Stochastic Geophysical Fluid Dynamics, Oberwolfach, Germany. |
| June 2022 | Inviscid Limit for Stochastic Navier–Stokes Equations in 2D Domains with Boundary, Third Italian Meeting of Probability and Mathematical Statistics, Bologna, Italy. |
| April 2022 | Inviscid Limit for Stochastic Navier–Stokes Equations in 2D Domains with Boundary, SPASS Seminars in Probability, Stochastic Analysis and Statistics, Pisa, Italy. |
Teaching
Selected teaching activities: information to be provided by the member.
