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

Grimshaw, Roger; Pelinovsky, Dmitry

RedOstrovskyAIMS_10.pdf (203.29 kB)

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

journal contribution

posted on 2018-03-14, 14:52 authored by Roger Grimshaw, Dmitry Pelinovsky

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.

History

School

Science

Department

Mathematical Sciences

Citation

GRIMSHAW, R.H.J. and PELINOVSKY, D., 2014. Global existence of small-norm solutions in the reduced Ostrovsky equation. Discrete and Continuous Dynamical Systems - A, 34 (2), pp.557-566.

Publisher

American Institute of Mathematical Sciences

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2014

Notes

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - A following peer review. The definitive publisher-authenticated version GRIMSHAW, R.H.J. and PELINOVSKY, D., 2014. Global existence of small-norm solutions in the reduced Ostrovsky equation. Discrete and Continuous Dynamical Systems - A, 34 (2), pp.557-566 is available online at: https://doi.org/10.3934/dcds.2014.34.557.