Gianluca Crippa

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20232025

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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…

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

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