Pullback $\mathcal{D}$-attractors for the non-autonomous Newton-Boussinesq equation in two-dimensional bounded domain

Xue-Li Song; Yan-Ren Hou

doi:10.3934/dcds.2012.32.991

Article Contents

2012, Volume 32, Issue 3: 991-1009. Doi: 10.3934/dcds.2012.32.991

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Pullback $\mathcal{D}$-attractors for the non-autonomous Newton-Boussinesq equation in two-dimensional bounded domain

Xue-Li Song^1, and
Yan-Ren Hou^1,

1.
College of science, Xi’an Jiaotong University, Xi’an, 710049

Received: August 31, 2010

Revised: April 30, 2011

Published: February 2012

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Abstract

We investigate the asymptotic behavior of solutions of a class of non-autonomous Newton-Boussinesq equation in two-dimensional bounded domain. The existence of pullback global attractors is proved in $L^2(\Omega)\times L^2(\Omega)$ and $H^1(\Omega)\times H^1(\Omega)$, respectively.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 35B41, 37L30.

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References

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