4:00–5:00 pm
Eckhart Hall Room 207-A
Defocusing Singularities and Compressible Fluids
Abstract:
The Non Linear Schrodinger equation with defocusing non linearity is a classical model for which singularity formation was explicitely conjectured not to occur in the energy super critical range. We will claim the opposite: in some regimes, blow up can occur. The structure of this new class of singularities is deeply related to compressible fluid mechanics and the description of large compressible shock waves, in connection with a classical problem: how may viscosity influence the formation of fluid singularities? I will present a series of joint works with Merle (IHES), Rodnianski (Princeton) and Szeftel (Paris) which open a breach for the study of large fluid singularities.
