Title: From Instability to Singularity Formation in Incompressible FluidsAbstract: In this talk, I will first review the singularity formation problem in incompressible fluid dynamics, describing how particle transport poses the main challenge in constructing blow-up solutions for the 3d incompressible Euler equations. I will then outline a new mechanism that allows us to overcome the effects of […]

Title: On linear and non-linear stability of collisionless systems on black hole exteriors.  Abstract:  I will present upcoming linear and non-linear stability results for collisionless systems on spherically symmetric black holes. On the one hand, I will discuss the decay properties of massive Vlasov fields on the exterior of Schwarzschild spacetime. On the other hand, I will discuss […]