A survival guide for feeble fish

Burago, D.; Ivanov, S.; Novikov, A.

doi:10.1090/spmj/1480

A survival guide for feeble fish
HTML articles powered by AMS MathViewer

by D. Burago, S. Ivanov and A. Novikov

St. Petersburg Math. J. 29 (2018), 33-41

DOI: https://doi.org/10.1090/spmj/1480

Published electronically: December 27, 2017

PDF | Request permission

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.

References

Pierre Cardaliaguet and Panagiotis E. Souganidis, Homogenization and enhancement of the $G$-equation in random environments, Comm. Pure Appl. Math. 66 (2013), no. 10, 1582–1628. MR 3084699, DOI 10.1002/cpa.21449
Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
James Nolen and Alexei Novikov, Homogenization of the G-equation with incompressible random drift in two dimensions, Commun. Math. Sci. 9 (2011), no. 2, 561–582. MR 2815685
Norbert Peters, Turbulent combustion, Cambridge Monographs on Mechanics, Cambridge University Press, Cambridge, 2000. MR 1792350, DOI 10.1017/CBO9780511612701
John D. Buckmaster (ed.), The mathematics of combustion, Frontiers in Applied Mathematics, vol. 2, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1985. MR 806548, DOI 10.1137/1.9781611971064