Аннотация:
As avid anglers, the authors are interested in the survival chances of fish in turbulent oceans. This paper addresses this question mathematically. It is shown that a fish with bounded aquatic locomotion speed can reach any point in the ocean if the fluid velocity is incompressible, bounded, and has small mean drift.
Ключевые слова:
G-equation, small controls, incompressible flow, reachability.
The first author was partially supported by NSF grant DMS-1205597. The second author was partially supported by
RFBR grant 14-01-00062. The third author was partially supported by NSF grant DMS-1515187.
Образец цитирования:
D. Burago, S. Ivanov, A. Novikov, “A survival guide for feeble fish”, Алгебра и анализ, 29:1 (2017), 49–59; St. Petersburg Math. J., 29:1 (2018), 33–41
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1521
https://www.mathnet.ru/rus/aa/v29/i1/p49
Эта публикация цитируется в следующих 3 статьяx:
Sergey Kryzhevich, Eugene Stepanov, Springer Proceedings in Mathematics & Statistics, 407, Dynamic Control and Optimization, 2022, 3
Burago D., Ivanov S., Novikov A., “Feeble Fish in Time-Dependent Waters and Homogenization of the G-Equation”, Commun. Pure Appl. Math., 73:7 (2020), 1453–1489
S. Kryzhevich, E. Stepanov, “The saga of a fish: from a survival guide to closing lemmas”, J. Differ. Equ., 267:6 (2019), 3442–3474