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

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  • 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 $H^3(\mathbb{R})$. 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.
    Mathematics Subject Classification: Primary: 35A01; Secondary: 35Q35.


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