Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-20T12:25:52.403Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Benney equation

Published online by Cambridge University Press:  04 November 2009

Amin Esfahani
Amin Esfahani
Affiliation:
Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, Rio de Janeiro, RJ, Brazil, (amin@impa.br)
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the Benney equation and show that the associated initial-value problem is locally well-posed in Sobolev spaces Hs(ℝ2) for s > −2. Furthermore, we use a priori estimates to establish the global well-posedness for s ≥ 0. We also prove that these results are in some sense sharp. In addition, we obtain some exact travelling-wave solutions of the equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 6 , December 2009 , pp. 1121 - 1144
Copyright
Copyright © Royal Society of Edinburgh 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)