The finite dimensions and determining modes of the global attractor for   2d Boussinesq equations with fractional Laplacian
  In this article, we prove the finite dimensionality of the global attractor and estimate the numbers of the determining modes for the 2D Boussinesq system in a periodic channel with fractional Laplacian in subcritical case. 
Aimin Huang and Wenru Huo
math.AP