We will be interested in the solutions to the Vlasov-Maxwell system arising from sufficiently small and regular data. In particular, we will compare their asymptotic behavior with the ones of the solutions to the linearised system. Even if the electromagnetic fields have a nontrivial memory effect, they enjoy linear scattering since they approach, for large time, a solution to the vacuum...
The existence of multi black hole solutions in asymptotically flat spacetimes is one of the expectation from the final state conjecture. In this talk, I will present preliminary works in this direction via a semilinear toy model in dimension 3. In particular, I show 1) an algorithm to construct approximate solutions to the energy critical wave equation that converge to a sum of solitons at an...
The study of wave propagation on black hole spacetimes has been an intense field of research in the past decades. This interest has been driven by the stability problem for black holes and by questions related to scattering theory. On Kerr black holes, the analysis of Maxwell's equations and the equations of linearized gravity, can be simplified by introducing the Teukolsky equation, which...
We are interested in the dynamical behaviour of relativistic fluids towards the expanding direction of cosmological spacetimes.
It is known that the expansion of spacetime induces a friction-like term in the fluid equation, which can prevent the formation of shocks, yielding future global solutions for small initial data.
This phenomenon is referred to as fluid stabilization. While this...
