Quasi-periodic solutions for some ill-posed Hamiltonian evolution equations

PDE Seminar
Tuesday, November 20, 2012 - 3:05pm
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
We prove an a-posteriori KAM theorem which applies to some ill-posed Hamiltonian equations. We show that given an approximate solution of an invariance equation which also satisfies some non-degeneracy conditions, there is a true solution nearby. Furthermore, the solution is "whiskered" in the sense that it has stable and unstable directions. We do not assume that the equation defines an evolution equation. Some examples are the Boussinesq equation (and system) and the elliptic equations in cylindrical domains. This is joint work with Y. Sire. Related work with E. Fontich and Y. Sire.