吸引子是无穷维动力系统中的一个重要概念，用来刻画偏微分方程解的长时间行为。鉴于Newton-Boussinesq方程是一类很重要的流体力学方程，但目前其解的渐近行为研究成果很少, 本项目将对二维Newton-Boussinesq方程弱解的几种吸引子的存在性进行研究。分别借助半群理论、过程理论、共圈映射理论对二维有界区域和管道流区域中Newton-Boussinesq方程弱解的全局吸引子和指数吸引子、一致吸引子、拉回吸引子的存在性进行探讨。当吸引子不存在时，将给出这些吸引子存在的条件。本项目的研究在Newton-Boussinesq方程理论方面具有良好的学术意义.

Attractor, which is a very important conception in infinite dimensional dynamical system, can be used to decribe the long time dynamical behavior of solutions of partial differential equations. Noting that Newton-Boussinesq equation is an important fluid mechanics equation, however, in terms of the asymptotic behavior of solutions for this equation, the conclusion is very less. The current proposed project prepares to investigate the existence of several kinds of attractors for two-dimensional Newton-Boussinesq equation. Applying semigroup theory, processes theory and cocycle mapping theory, the existence of global attractors(exponential attractors), uniform attractors and pullback attractors of two-dimensional Newton-Boussinesq equation in two-dimensional bounded and channel domains are discussed, respectively. If these attractors do not exist, the condition of existence for these attractors will be given. The research possesses high academic significance in respect of Newton-Boussinesq equation theory.