The global attractor of  the damped, forced generalized Korteweg de Vries-Benjamin-Ono equation in  $L^2$

Boling Guo; Zhaohui Huo

doi:10.3934/dcds.2006.16.121

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2006, Volume 16, Issue 1: 121-136. Doi: 10.3934/dcds.2006.16.121

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The global attractor of the damped, forced generalized Korteweg de Vries-Benjamin-Ono equation in $L^2$

Boling Guo^1, and
Zhaohui Huo^2,

1.
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088
2.
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080

Received: May 2005

Revised: March 2006

Published: March 2006

Abstract / Introduction Related Papers Cited by

Abstract

The existence of the global attractor of the damped, forced generalized KdV-Benjamin-Ono equation in $L^2( \mathbb{R})$ is proved for forces in $L^2( \mathbb{R})$. Moreover, the global attractor in $L^2( \mathbb{R})$ is actually a compact set in $H^3( \mathbb{R})$.

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Mathematics Subject Classification: 35Q53, 35B40, 37L50.

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The global attractor of the damped, forced generalized Korteweg de Vries-Benjamin-Ono equation in $L^2$

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