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St. Petersburg Mathematical Journal

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A survival guide for feeble fish


Authors: D. Burago, S. Ivanov and A. Novikov
Original publication: Algebra i Analiz, tom 29 (2017), nomer 1.
Journal: St. Petersburg Math. J. 29 (2018), 33-41
MSC (2010): Primary 49K15
DOI: https://doi.org/10.1090/spmj/1480
Published electronically: December 27, 2017
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Abstract: 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.


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Additional Information

D. Burago
Affiliation: The Pennsylvania State University Department of Mathematics University Park, PA 16802 USA
Email: burago@math.psu.edu

S. Ivanov
Affiliation: St. Petersburg Branch Steklov Institute of Mathematics Russian Academy of Sciences Fontanka 27 191023 St. Petersburg Russia
Email: svivanov@pdmi.ras.ru

A. Novikov
Affiliation: The Pennsylvania State University Department of Mathematics University Park, PA 16802 USA
Email: anovikov@math.psu.edu

DOI: https://doi.org/10.1090/spmj/1480
Keywords: G-equation, small controls, incompressible flow, reachability
Received by editor(s): May 15, 2016
Published electronically: December 27, 2017
Additional Notes: 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
Dedicated: Dedicated to Yu. D. Burago on the occasion of his 80th birthday
Article copyright: © Copyright 2017 American Mathematical Society

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