Patrick Gerard (Orsay)

The half-wave maps equation and Hankel operators

I will introduce an energy critical quasilinear hyperbolic evolution system on maps from the line into the two-dimensional sphere. I will show that this system admits a Lax pair involving Hankel operators with some matrix symbols, and I will stress some consequences of this result for the corresponding dynamics.
This is a joint work with Enno Lenzmann (Basel).