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