# Fourth Kinetic Theory Seminar

### 2 May 2023

We are pleased to announce the fourth edition of the Kinetic Theory Seminar (ETH Zurich, 26th May). This edition will celebrate the achievements of women in the field in the framework of the May12 initiative.

This seminar series organized by Mikaela Iacobelli (ETH Zurich) and Chiara Saffirio (UniBas), brings together researchers interested in kinetic theory from the Zurich and Basel area. There is one event per semester, alternating locations between the ETH Zurich and the University of Basel.

**Date:** Friday, 26th May 2023

**Time: **2:15 p.m. – 5:00 p.m. 2.15-3.15 (First talk and discussions. 3.15-4.00 Coffee Break 4.00-5.00 Second talk and discussions).

**Room: **ETH Zurich, HG G 19.2

**Speakers: **

**Prof. Giada Basile **(Sapienza University of Rome)

**Title: **Asymptotic probability of energy increasing paths for the Kac's walk.

**Abstract: **I will present some recent results on large deviations for binary collision stochastic models. The paradigmatic model is the Kac’s walk, described, in the kinetic limit, by the homogeneous Boltzmann equation. I will discuss the large deviation principle and I will exhibit some atypical paths that violate energy conservation. In particular, I will compute the asymptotic probability of energy increasing paths. Joint work with L. Bertini, D. Benedetto and E. Caglioti.

**Dr. Megan Griffin-Pickering (UCL) **

**Title: **The Vlasov-Poisson system for ions: recent developments on the quasi-neutral limit

**Abstract: **Vlasov-Poisson systems are a well-known class of kinetic models for plasma. The precise structure of the model differs according to which species of particle (electrons or ions) it describes, with the `classical’ version of the system describing electrons. The model for ions, however, has been studied only more recently, owing to an additional exponential nonlinearity in the equation for the electrostatic potential that creates several mathematical difficulties not encountered in the electron case.

The Debye length is a characteristic length scale of a plasma describing the scale of electrostatic interaction. In real plasmas this length is typically very small, and in physics applications frequently assumed to be very close to zero. This motivates the study of the limiting behaviour of Vlasov-Poisson type systems as the Debye length tends to zero relative to the observation scale—known as the ‘quasi-neutral’ limit. In the case of the ionic model, the formal limit is the kinetic isothermal Euler system; however, this limit is highly non-trivial to justify rigorously and known to be false in some cases without very strong regularity conditions and/or structural conditions.

I will discuss recent developments in the theory of the quasi-neutral limit for the ionic Vlasov-Poisson system—in particular, recent results for a certain class of rough (L^\infty) data that may be expressed as perturbations of an analytic function, small in the sense of Monge-Kantorovich-Wasserstein distances. The smallness of the perturbation that we require is much less restrictive than in the previously known results.

Based on joint works with Mikaela Iacobelli (ETH Zurich).

This event has been registered on the May12 website