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| Title: | Global existence of small-norm solutions in the reduced Ostrovsky equation |
| Authors: | Grimshaw, Roger H.J.
Pelinovsky, Dmitry |
| Keywords: | Reduced Ostrovsky equation
Tzitzeica equation
Wave breaking
Conserved quantities
Global existence |
| Issue Date: | 2014 |
| Publisher: | American Institute of 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. |
| Abstract: | 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. |
| Description: | 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. |
| Version: | Accepted for publication |
| DOI: | 10.3934/dcds.2014.34.557 |
| URI: | https://dspace.lboro.ac.uk/2134/32205 |
| Publisher Link: | https://doi.org/10.3934/dcds.2014.34.557 |
| ISSN: | 1078-0947 |
| Appears in Collections: | Published Articles (Maths)
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