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Journal Articles SIAM Journal on Mathematical Analysis Year : 2020

On a Damped Szegö Equation (With an Appendix in Collaboration With Christian Klein)

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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.

Dates and versions

hal-03130243 , version 1 (03-02-2021)

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Patrick Gérard, Sandrine Grellier, Christian Klein. On a Damped Szegö Equation (With an Appendix in Collaboration With Christian Klein). SIAM Journal on Mathematical Analysis, 2020, 52 (5), pp.4391-4420. ⟨10.1137/19M1299189⟩. ⟨hal-03130243⟩
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