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

Roger Grimshaw; Dmitry Pelinovsky

doi:10.3934/dcds.2014.34.557

Article Contents

2014, Volume 34, Issue 2: 557-566. Doi: 10.3934/dcds.2014.34.557

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

Roger Grimshaw^1, and
Dmitry Pelinovsky^2,

1.
Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU
2.
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1

Received: October 31, 2012

Revised: March 31, 2013

Published: January 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 35A01; Secondary: 35Q35.

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