Wave breaking in the Ostrovsky--Hunter equation

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.

22 pages, 5 figures

References in corpus (2)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Global well-posedness of the short-pulse and sine-Gordon equations in energy space

Cited by in corpus (8)

• Hamiltonian Structures for the Ostrovsky-Vakhnenko Equation
• Blowing-up solutions of the time-fractional dispersive equations
• Integrable semi-discretizations of the reduced Ostrovsky equation
• Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
• A convergent finite difference scheme for the Ostrovsky--Hunter equation with Dirichlet boundary conditions
• A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue
• Large time asymptotics of solutions to the short-pulse equation
• One-sided Hölder regularity of global weak solutions of negative order dispersive equations