Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models

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August 2006, 15(3): 777-809. doi: 10.3934/dcds.2006.15.777

Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models

Igor Chueshov ^1, and Irena Lasiecka ^2,

1.	Kharkov University, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkov, Ukraine
2.	University of Virginia, Department of Mathematics, Charlottesville, VA 22901

Received March 2005 Revised August 2005 Published April 2006

Abstract
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We study dynamics of a class of nonlinear Kirchhoff-Boussinesq plate models. The main results of the paper are: (i) existence and uniqueness of weak (finite energy) solutions, (ii) existence of weakly compact attractors.

Keywords: 2D Boussinesq models, weak well-posedness, global attractors..

Mathematics Subject Classification: Primary: 60H25, 47H10; Secondary: 34D3.

Citation: Igor Chueshov, Irena Lasiecka. Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 777-809. doi: 10.3934/dcds.2006.15.777

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