二维磁微极流体方程一致吸引子的分形维数

Fractal Dimension of Uniform Attractor for 2D Magneto-Micropolar Fluid Equations

研究了有界域上二维磁微极流体方程一致吸引子分形维数的有限性.在外力概周期的条件下,首先,得到方程解的一致估计,其次,证明了方程解的Lipschitz连续性与解的光滑特性.最后,证明了非自治磁微极流体方程的一致吸引子具有有限的分形维数,从而有效刻画了二维磁微极流体方程一致吸引子的几何结构.

The boundedness of fractal dimension of uniform attractor for 2D magneto-micropolar fluid equations in a bounded domain is investigated.The uniform estimates of the solutions for the equation is firstly obtained under the assumption of almost periodic external force,and then the Lipschitz continuity and smoothing property of the solution are proved.Finally,it is proved that the fractal dimension of the uniform attractor for the non-autonomous magneto-micropolar fluid equations is finite,thus the geometry of the uniform attractor of the 2D magneto-micropolar fluid equation is effectively characterized.