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Global existence of small-norm solutions in the reduced Ostrovsky equation
Discrete and Continuous Dynamical Systems. Series A
We use a novel transformation of the reduced Ostrovsky equation to the integrable Tzitzéica 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. 2010 Mathematics Subject Classification. Primary: 35A01; Secondary: 35Q35.doi:10.3934/dcds.2014.34.557 fatcat:bripuelnxvdzdlewans4bcwdsm