On a damped Szego equation (with an appendix in collaboration with Christian Klein)

Patrick Gérard (1) , Sandrine Grellier (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We investigate how damping the lowest Fourier mode modifies the dynamics of the cubic Szegő equation. We show that there is a nonempty open subset of initial data generating trajec-tories 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 generalisation of this picture to more general initial data.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]

Patrick Gérard, Sandrine Grellier. On a damped Szego equation (with an appendix in collaboration with Christian Klein). SIAM Journal on Mathematical Analysis, 2020, 52 (5), pp.4391-4420. ⟨10.1137/19M1299189⟩. ⟨hal-02358383⟩