The global attractor of the 2d Boussinesq equations with fractional Laplacian in subcritical case

Wenru  Huo; Aimin  Huang

doi:10.3934/dcdsb.2016059

Article Contents

2016, Volume 21, Issue 8: 2531-2550. Doi: 10.3934/dcdsb.2016059

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The global attractor of the 2d Boussinesq equations with fractional Laplacian in subcritical case

Wenru Huo^1, and
Aimin Huang^2,

1.
The Department of Mathematics, Indiana University, 831 East Third Street, Rawles Hall, Bloomington, Indiana 47405
2.
The Institute for Scientic Computing and Applied Mathematics, Indiana University, 831 East Third Street, Rawles Hall, Bloomington, Indiana 47405

Received: August 2015

Revised: April 2016

Published: October 2016

Abstract / Introduction Related Papers Cited by

Abstract

We prove global well-posedness of strong solutions and existence of the global attractor for the 2D Boussinesq system in a periodic channel with fractional Laplacian in subcritical case. The analysis reveals a relation between the Laplacian exponent and the regularity of the spaces of velocity and temperature.

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Mathematics Subject Classification: Primary: 35Q86, 35R11; Secondary: 34D45.

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