Évènement

Yoan TARDY
École polytechnique

Date(s) : 04/03/2025   iCal
14h30 - 15h30

We study a particle system naturally associated to the 2-dimensional Keller-Segel equation.
It consists of N Brownian particles in the plane,
interacting through a binary attraction in θ/(Nr),
where r stands for the distance between two particles.
When the intensity θ of this attraction is greater than 2,
this particle system explodes in finite time.
We assume that N>3θ and study in details what happens near explosion.
There are two slightly different scenarios,
depending on the values of N and θ, here is one:
at explosion, a cluster consisting of precisely k0 particles emerges,
for some deterministic k0≥7 depending on N and θ.
Just before explosion, there are infinitely many (k0−1)-ary collisions.
There are also infinitely many (k0−2)-ary collisions before each (k0−1)-ary collision.
And there are infinitely many binary collisions before each (k0−2)-ary collision.
Finally, collisions of subsets of 3,…,k0−3 particles never occur.
The other scenario is similar except that there are no (k0−2)-ary collisions.

Emplacement
I2M Saint-Charles - Salle de séminaire

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