On the Attractor for the Semi-Dissipative Boussinesq Equations

2015/07/01 by Biswas, Animikh, Foias, Ciprian, Larios, Adam
#35B41 #35K55 #35Q35 #35Q86 #76F05 #76F25 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1507.00080

Abstract

In this article, we study the long time behavior of solutions of a variant of the Boussinesq system in which the equation for the velocity is parabolic while the equation for the temperature is hyperbolic. We prove that the system has a global attractor which retains some of the properties of the global attractors for the 2D and 3D Navier-Stokes equations. Moreover, this attractor contains infinitely many invariant manifolds in which several universal properties of the Batchelor, Kraichnan, Leith theory of turbulence are potentially present.

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