Y. Liu, D. Pelinovsky and A. Sakovich

Wave breaking in the Ostrovsky-Hunter equation

SIAM Journal of Mathematical Analysis 42, 1967–1985 (2010)

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.

Ostrovsky-Hunter equation, wave breaking, well-posedness, conserved quantities, method of characteristics.