On generalized Benjamin type equations

Felipe Linares; M. Scialom

doi:10.3934/dcds.2005.12.161

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2005, Volume 12, Issue 1: 161-174. Doi: 10.3934/dcds.2005.12.161

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On generalized Benjamin type equations

Felipe Linares^1, and
M. Scialom^2,

1.
IMPA, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320
2.
IMECC-UNICAMP, Campinas, 13081-970

Received: April 30, 2003

Revised: May 31, 2004

Published: March 2005

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Abstract

We establish local and global well-posedness for the initial value problem associated to the generalized Benjamin equation and generalizations of this in the energy space. We also studied the limit process of solutions when the surface tension is becoming small. To establish these results we make use of sharp theory developed to the study of the generalized Korteweg-de Vries equation.

Keywords:

Benjamin equation,
well-posedness.

Mathematics Subject Classification: 35Q53, 35Q51, 76B15.

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