Upcoming events

Maxwell Joint Seminar in PDE: Nicolas Burq (Paris), Pierre Raphael (Cambridge)

Location: ICMS, Bayes Centre Lecture Theatre 5.10

Description: 14:00 - 15:00 Pierre Raphael (University of Cambridge)Title: On singularity formation for non linear PDE'sAbstract: The question of the formation of singularities in non linear PDE’s in connection with energy concentration mechanisms has produced a huge amount of litterature, both in mathematics and physics. Yet, despite some substantial progress in the last twenty years and the development of numerical methods, basic questions remain completely open like the singularity formation problem in incompressible fluid dynamics. In all known singularity formation problems, self similar solutions or stationary soliton like solutions are fundamental structures underlying the concentration of energy mechanisms. In a recent joint work with Merle (IHES), Rodnianski (Princeton) and Szeftel (Sorbonne Universite), we show how singularity formation can still occur despite the absence of such special solutions with applications to the first description of implosion for a viscous three dimensional compressible fluid, and the discovery of highly oscillatory blow up solutions to the energy super critical non linear Schrodinger equation which answer negatively a conjecture formulated by Bourgain in 2000.15:00 - 16:00 Nicolas Burq (Universite Paris-Sud)  Title: Geometry and concentration properties of solutions to PDEsAbstract: In this talk I will present recent results on concentration properties of solutions to wave or Schrödinger (time dependent or not) equations. For the waves I will show how some precise analysis of these concentration properties can give an answer to a longstanding question of controllability for waves on the disc, while for Schrödinger, I will show how one can take benefit from the global properties of the geodesic flow to exhibit some particular behaviours.