English

On the Attractor for the Semi-Dissipative Boussinesq Equations

Mathematical Physics 2015-07-02 v1 Analysis of PDEs math.MP

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.

Keywords

Cite

@article{arxiv.1507.00080,
  title  = {On the Attractor for the Semi-Dissipative Boussinesq Equations},
  author = {Animikh Biswas and Ciprian Foias and Adam Larios},
  journal= {arXiv preprint arXiv:1507.00080},
  year   = {2015}
}