DG-MP-PDE Seminar: Benoit Pausader (Brown University)

We will prove that solutions to the defocusing energy-critical Schrodinger equations are global in the hyperbolic space H^3. The relevance of the energy-critical case is that in this case, one needs to understand how to take into account the scaling limits of the equation. In particular, one needs to see how to connect solutions to the corresponding equation on a Euclidian space to solutions of the original equation which concentrate as they evolve. To try and understand the influence of the geometry, we will also look at some results on other spaces in the other directions (the volume of balls grows slowly as the radius goes to infinity). This is a joint work with A. Ionescu and G. Staffilani.