Events

Date: 25 February 2025   Time: 14:00 - 15:00     

Location: MB503

Radiative properties of collisionless matter in isolated charged systems

The Vlasov--Poisson system describes the evolution of an ensemble of either:

1. Electrically charged particles, interacting via an electrostatic Coulomb force;

2. Self-gravitating particles, interacting via a Newtonian gravitational force.

In 3 space dimensions, for isolated systems, dispersive solutions asymptotically exhibit logarithmically corrected linear behaviour, i.e. such solutions ``scatter'' in a modified sense (in contrast to 4 space dimensions and higher, where such solutions asymptotically behave linearly).

I will discuss a new proof of well posedness of the inverse modified scattering problem: for every suitable scattering profile, there exists a solution of Vlasov--Poisson which disperses and scatters, in a modified sense, to this profile. Further, as a consequence of the proof, the solutions are shown to admit a ``polyhomogeneous expansion'', to any finite but arbitrarily high order, with coefficients given explicitly in terms of the scattering profile.

I will then discuss a generalisation to the study of the electromagnetic radiation created by a collection of infalling particles in the context of the Vlasov--Maxwell system. This is joint work with Volker Schlue (Melbourne).