Patrick Gerard (University of Paris-Sud)

BMO solutions of the cubic Szego equation

Abstract: The cubic Szego equation is a recently introduced toy model of a Hamiltonian evolution PDE with lack of dispersion. I will show how the Lax pair structure of this equation allows to define a global Hamiltonian flow on the Hardy version of John-Nirenberg's BMO space on the circle, and describe some qualitative properties of these singular solutions.