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

Roger Grimshaw; Dmitry Pelinovsky

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

Exactly Solvable and Integrable Systems 2013-04-08 v2 Analysis of PDEs

Authors: Roger Grimshaw , Dmitry Pelinovsky

Abstract

We use a novel transformation of the reduced Ostrovsky equation to the integrable Tzitz\'eica equation and prove global existence of small-norm solutions in Sobolev space $H^3(R)$ . 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.

Keywords

reduced Ostrovsky equation Tzitz\'eica equation small-norm solutions global existence finite-time wave breaking Sobolev space

Cite

@article{arxiv.1210.6526,
  title  = {Global existence of small-norm solutions in the reduced Ostrovsky equation},
  author = {Roger Grimshaw and Dmitry Pelinovsky},
  journal= {arXiv preprint arXiv:1210.6526},
  year   = {2013}
}

Comments

11 pages; 1 figure

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