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 Szegö 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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Information & Authors
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Published In
SIAM Journal on Mathematical Analysis
Pages: 4391 - 4420
DOI: 10.1137/19M1299189
ISSN (online): 1095-7154
Copyright
© 2020, Society for Industrial and Applied Mathematics.
History
Submitted: 12 November 2019
Accepted: 29 June 2020
Published online: 17 September 2020
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