Long-time asymptotic behavior of two-dimensional  dissipativeBoussinesq systems

Min Chen; Olivier Goubet

doi:10.3934/dcdss.2009.2.37

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2009, Volume 2, Issue 1: 37-53. Doi: 10.3934/dcdss.2009.2.37

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Long-time asymptotic behavior of two-dimensional dissipative Boussinesq systems

Min Chen^1, and
Olivier Goubet^2,

1.
Department of Mathematics, Purdue University, West Lafayette, IN 47907
2.
Universite de Picardie Jules Verne, LAMFA UMR 7352, 33 rue Saint-Leu, 80039 Amiens cedex

Received: January 31, 2008

Revised: June 30, 2008

Published: February 2009

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Abstract

In this article, we consider the two-dimensional dissipative Boussinesq systems which model surface waves in three space dimensions. The long time asymptotics of the solutions for a large class of such systems are obtained rigorously for small initial data.

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Mathematics Subject Classification: Primary: 35Q35, 35Q53,76B15; Secondary: 65M70.

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