带有记忆的Boussinesq方程指数吸引子的存在性

考虑带有记忆的Boussinesq方程解的长时间动力学行为. 首先通过引入新的变量将原方程转化为一个动力系统, 然后利用算子分解技巧及历史空间上的紧性定理证明所研究问题对应解半群的紧性; 最后结合指数吸引子的存在性得到记忆型Boussinesq方程的指数吸引子, 从而获得了该问题全局吸引子的有限分形维数.

Existence of Exponential Attractors forBoussinesq Equations with Memory

We considered the long time dynamical behavior of solutions of Boussinesq equations with memory. Firstly, the original equation wastransformed into a dynamical system by introducing a new variable. Secondly, thecompactness of corresponding solutions semigroups associated with problem was proved by using the technique of operator decomposition and the compactness theorem on historical spaces. Finally, the exponential attractor of the memory typeBoussinesq equation was obtained by combining the existence of the exponential attractor, and the finite fractal dimension of the global attractor of the problem was obtained.