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R. Grimshaw and D.E. Pelinovsky

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

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

**Abstract:**

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 H^{3}(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.

**Keywords:**

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