Location:

Spiegelgasse 1, Lecture Room 00.003

## Seminar Analysis: Mikaela Iacobelli (ETH Zürich)

**Recent results on singular limits for Vlasov-Poisson**

The Vlasov-Poisson system is a kinetic equation that models collisionless plasma. A plasma has a characteristic scale called the Debye length, which is typically much shorter than the scale of observation. In this case the plasma is called ‘quasineutral’. This motivates studying the limit in which the ratio between the Debye length and the observation scale tends to zero. Under this scaling, the formal limit of the Vlasov-Poisson system is the Kinetic Isothermal Euler system.

The Vlasov-Poisson system itself can formally be derived as the limit of a system of ODEs describing the dynamics of a system of N interacting particles, as the number of particles approaches infinity. The rigorous justification of this mean field limit remains a fundamental open problem.

In this talk we present how the mean field and quasineutral limits can be combined to derive the Kinetic Isothermal Euler system from a regularised particle model.

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