Turbulent cascades for a family of damped Szegő equations
Gérard P, Grellier S, He Z (2022)
Nonlinearity 35(9): 4820-4849.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Gérard, Patrick;
Grellier, Sandrine;
He, ZihuiUniBi
Einrichtung
Abstract / Bemerkung
In this paper, we study the transfer of energy from low to high frequencies for a family of damped Szegő equations. The cubic Szegő equation has been introduced as a toy model for a totally non-dispersive degenerate Hamiltonian equation. It is a completely integrable system which develops growth of high Sobolev norms, detecting transfer of energy and hence cascades phenomena. Here, we consider a two-parameter family of variants of the cubic Szegő equation and prove that, adding a damping term unexpectedly promotes the existence of turbulent cascades. Furthermore, we give a panorama of the dynamics for such equations on a six-dimensional submanifold.
Stichworte
Analysis of PDEs (math.AP);
Classical Analysis and ODEs (math.CA);
FOS: Mathematics;
FOS: Mathematics
Erscheinungsjahr
2022
Zeitschriftentitel
Nonlinearity
Band
35
Ausgabe
9
Seite(n)
4820-4849
Urheberrecht / Lizenzen
ISSN
0951-7715
eISSN
1361-6544
Page URI
https://pub.uni-bielefeld.de/record/2962777
Zitieren
Gérard P, Grellier S, He Z. Turbulent cascades for a family of damped Szegő equations. Nonlinearity . 2022;35(9):4820-4849.
Gérard, P., Grellier, S., & He, Z. (2022). Turbulent cascades for a family of damped Szegő equations. Nonlinearity , 35(9), 4820-4849. https://doi.org/10.1088/1361-6544/ac7e13
Gérard, Patrick, Grellier, Sandrine, and He, Zihui. 2022. “Turbulent cascades for a family of damped Szegő equations”. Nonlinearity 35 (9): 4820-4849.
Gérard, P., Grellier, S., and He, Z. (2022). Turbulent cascades for a family of damped Szegő equations. Nonlinearity 35, 4820-4849.
Gérard, P., Grellier, S., & He, Z., 2022. Turbulent cascades for a family of damped Szegő equations. Nonlinearity , 35(9), p 4820-4849.
P. Gérard, S. Grellier, and Z. He, “Turbulent cascades for a family of damped Szegő equations”, Nonlinearity , vol. 35, 2022, pp. 4820-4849.
Gérard, P., Grellier, S., He, Z.: Turbulent cascades for a family of damped Szegő equations. Nonlinearity . 35, 4820-4849 (2022).
Gérard, Patrick, Grellier, Sandrine, and He, Zihui. “Turbulent cascades for a family of damped Szegő equations”. Nonlinearity 35.9 (2022): 4820-4849.
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arXiv: 2111.05247
Preprint: 10.48550/ARXIV.2111.05247
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