Feeble fish in time-dependent waters and homogenization of the G-equation

Dmitri Burago, Sergei Ivanov, Alexei Novikov

Published 2017-12-22Version 1

We study the following control problem. Fish with bounded aquatic locomotion speed swims in fast waters. Can the fish, under reasonable assumptions, get to a desired destination? It can, even if the flow is time-dependent. Moreover, given a prescribed sufficiently large time $t$, it can be there at exactly the time $t$. The major difference from our previous work is the time-dependence of the flow and an application to homogenization of the G-equation.