三维Ginzburg-Landau方程的吸引子的分形结构(英文)

The fractal structure of attractor for complex Ginzburg-Landau equation in three-dimensions

构造并证明了三维Ginzburg-Landau方程(CGL)ut=ρu+(1+iγ)Δu-(1+iμ)|u|2σu整体吸引子紧的分形结构的存在性,进一步得到了吸引子的一个指数型的紧的分形局部化逼近序列,从而改进并精细了该方程关于吸引子的有关结果.

In this paper,the complex GinzburgLandau equation(CGL) in three spatial dimensions ut=ρu+(1+iγ)Δu-(1+iμ)｜u｜2σu is considered.The compact fractal structure of global attractor of CGL equation had been constructed and proved.Furture,an exponentially approximating sequence of compact fractal localizing sets of attractor had been found out. Therefore,the result about the attractor of CGL equation have been improved and sharped.