On a Damped Szegö Equation (With an Appendix in Collaboration With Christian Klein)
Abstract
We investigate how damping the lowest Fourier mode modifies the dynamics of the cubic Szego equation. We show that there is a nonempty open subset of initial data generating trajectories with high Sobolev norms tending to infinity. In addition, we give a complete picture of this phenomenon on a reduced phase space of dimension 6. An appendix is devoted to numerical simulations supporting the generalization of this picture to more general initial data.