Gianluca Crippa

activity

20232025

collaborators

4 papers

math.AP2025

Introduction to the theory of mixing for incompressible flows

Gianluca Crippa

In these lecture notes, we provide an introduction to the theory of mixing for incompressible flows from a PDE perspective. We discuss both the Lagrangian (ODE) and Eulerian (PDE,…

math.PR2025

Zero-noise selection and Large Deviations in $L_{t}^{\infty} L_{x}^{p}$ for the stochastic transport equation beyond DiPerna-Lions

Gianluca Crippa, Eliseo Luongo, Umberto Pappalettera

We consider $L_{t}^{\infty} L_{x}^{p}$ solutions of the stochastic transport equation with drift in $L_{t}^{\infty} W_{x}^{1, q}$ . We show strong existence and pathwise uniqueness of solutions in…

math.AP2024

Normal traces and applications to continuity equations on bounded domains

Gianluca Crippa, Luigi De Rosa, Marco Inversi +1

In this work, we study several properties of the normal Lebesgue trace of vector fields introduced by the second and third author in [22] in the context of the energy conservation…

math.AP2023

Existence and stability of weak solutions of the Vlasov--Poisson system in localized Yudovich spaces

Gianluca Crippa, Marco Inversi, Chiara Saffirio +1

We consider the Vlasov--Poisson system both in the repulsive (electrostatic potential) and in the attractive (gravitational potential) cases. In our first main theorem, we prove th…

Introduction to the theory of mixing for incompressible flows

Zero-noise selection and Large Deviations in Lt∞​Lxp​ for the stochastic transport equation beyond DiPerna-Lions

Normal traces and applications to continuity equations on bounded domains

Existence and stability of weak solutions of the Vlasov--Poisson system in localized Yudovich spaces

Zero-noise selection and Large Deviations in $L_{t}^{\infty} L_{x}^{p}$ for the stochastic transport equation beyond DiPerna-Lions