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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.
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https://hal.archives-ouvertes.fr/hal-03130243
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Submitted on : Wednesday, February 3, 2021 - 2:25:28 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM

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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, Society for Industrial and Applied Mathematics, 2020, 52 (5), pp.4391-4420. ⟨10.1137/19M1299189⟩. ⟨hal-03130243⟩

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