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On the Attractor for the Semi-Dissipative Boussinesq Equations

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.

preprint2015arXivOpen access
Animikh BiswasCiprian FoiasAdam Larios
math.APmath-phmath.MP
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Animikh BiswasCiprian FoiasAdam Larios

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