Dynamics of several point vortices for the lake equations
Hientzsch LE, Lacave C, Miot E (2023)
Transactions of the American Mathematical Society.
Zeitschriftenaufsatz
| E-Veröff. vor dem Druck | Englisch
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Autor*in
Hientzsch, Lars EricUniBi
;
Lacave, Christophe;
Miot, Evelyne
![](https://pub.uni-bielefeld.de/images/icon_orcid.png)
Einrichtung
Abstract / Bemerkung
The global asymptotic dynamics of point vortices for the lake equations is rigorously derived. Vorticity that is initially sharply concentrated around N distinct vortex centers is proven to remain concentrated for all times. Specifically, we prove weak concentration of the vorticity and in addition strong concentration in the direction of the steepest ascent of the depth function. As a consequence, we obtain the motion law of point vortices following at leading order the level lines of the depth function. The lack of strong localization in the second direction is linked to the vortex filamentation phenomena. The main result allows for any fixed number of vortices and general assumptions on the concentration property of the initial data to be considered. No further properties such as a specific profile or symmetry of the data are required. Vanishing topographies on the boundary are included in our analysis. Our method is inspired by recent results on the evolution of vortex rings in 3D axisymmetric incompressible fluids.
Erscheinungsjahr
2023
Zeitschriftentitel
Transactions of the American Mathematical Society
ISSN
0002-9947
eISSN
1088-6850
Page URI
https://pub.uni-bielefeld.de/record/2984070
Zitieren
Hientzsch LE, Lacave C, Miot E. Dynamics of several point vortices for the lake equations. Transactions of the American Mathematical Society. 2023.
Hientzsch, L. E., Lacave, C., & Miot, E. (2023). Dynamics of several point vortices for the lake equations. Transactions of the American Mathematical Society. https://doi.org/10.1090/tran/8995
Hientzsch, Lars Eric, Lacave, Christophe, and Miot, Evelyne. 2023. “Dynamics of several point vortices for the lake equations”. Transactions of the American Mathematical Society.
Hientzsch, L. E., Lacave, C., and Miot, E. (2023). Dynamics of several point vortices for the lake equations. Transactions of the American Mathematical Society.
Hientzsch, L.E., Lacave, C., & Miot, E., 2023. Dynamics of several point vortices for the lake equations. Transactions of the American Mathematical Society.
L.E. Hientzsch, C. Lacave, and E. Miot, “Dynamics of several point vortices for the lake equations”, Transactions of the American Mathematical Society, 2023.
Hientzsch, L.E., Lacave, C., Miot, E.: Dynamics of several point vortices for the lake equations. Transactions of the American Mathematical Society. (2023).
Hientzsch, Lars Eric, Lacave, Christophe, and Miot, Evelyne. “Dynamics of several point vortices for the lake equations”. Transactions of the American Mathematical Society (2023).
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