Asymptotic Behavior Of Boussinesq Equations

In this paper, we focus on the asymptotic behavior of the Boussinesq equations with random disturbances and without random disturbances which has important physical meaning, and get the existence conclusion of random attractor, uniform exponential attractors and pullback exponential attractor. The framework of this paper are following:In the first chapter, firstly we will introduces the background, the purpose, the significance of dynamical system at home and abroad and so on. Then we will give some important inequalities, such as Cauchy-Schwarz inequality and Gronwall inequality.In the second chapter, we will prove the existence of random attractor of Boussinesq lattice systems with multiplicative white noise and its Kolmogorov entropy.In the third chapter, we will prove the existence of uniform exponential attractors of non-autonomous Boussinesq lattice systems at the discretization of high dimensional space.In the forth chapter, we will prove the existence of pullback exponential attractors of non-autonomous Boussinesq lattice systems.In the fifth chapter, we summarize the conclusions obtained in this paper and put forward problem remaining to be solved.