R. Grimshaw and D.E. Pelinovsky

Global existence of small-norm solutions in the reduced Ostrovsky equation

Discrete Continuous Dynamical Systems Series A 34, 557-566 (2014)

We use a novel transformation of the reduced Ostrovsky equation to the integrable Tzitzeica equation and prove global existence of small-norm solutions in Sobolev space H3(R). This scenario is an alternative to finite-time wave breaking of large-norm solutions of the reduced Ostrovsky equation. We also discuss a sharp sufficient condition for the finite-time wave breaking.

Reduced Ostrovsky equation, short-pulse equation, Tzitzeica equation, conserved quantities, global existence, wave breaking.