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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)
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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

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