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

TL;DR

This paper proves the global existence of small-norm solutions for the reduced Ostrovsky equation by transforming it into an integrable equation, providing an alternative to wave breaking for large-norm solutions.

Contribution

It introduces a novel transformation linking the reduced Ostrovsky equation to the Tzitzéica equation and establishes global existence results for small-norm solutions.

Findings

Global existence of small-norm solutions in Sobolev space $H^3(R)$

A new transformation to an integrable equation

A sharp condition for finite-time wave breaking

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.