Journal article
Global existence of small-norm solutions in the reduced Ostrovsky equation
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.
Authors
Grimshaw R; Pelinovsky D
Journal
Discrete and Continuous Dynamical Systems, Vol. 34, No. 2, pp. 557–566
Publisher
American Institute of Mathematical Sciences (AIMS)
Publication Date
August 2013
DOI
10.3934/dcds.2014.34.557
ISSN
1078-0947