Wave breaking in the Ostrovsky--Hunter equation
Yue Liu, Dmitry Pelinovsky, and Anton Sakovich
TL;DR
This paper investigates wave breaking phenomena in the Ostrovsky--Hunter equation, providing conditions for wave blow-up, analyzing the blow-up rate, and illustrating finite-time wave breaking through numerical simulations.
Contribution
It establishes sufficient conditions for wave breaking in the Ostrovsky--Hunter equation and characterizes the blow-up rate using the method of characteristics.
Findings
Sufficient conditions for wave breaking are derived.
The blow-up rate at wave breaking is specified.
Numerical simulations illustrate finite-time wave breaking.
Abstract
The Ostrovsky--Hunter equation governs evolution of shallow water waves on a rotating fluid in the limit of small high-frequency dispersion. Sufficient conditions for the wave breaking in the Ostrovsky--Hunter equation are found both on an infinite line and in a periodic domain. Using the method of characteristics, we also specify the blow-up rate at which the waves break. Numerical illustrations of the finite-time wave breaking are given in a periodic domain.
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