Global Attractor For Three Dimensional Ginzburg-Landau Equation And The Estimate Of The Dimensionality Of Attractor

Ginzburg-Landau equation has very abundant physical background andconnotation, which appears at hydromechanics system, plasma propation andsuperconductor theory for a long history. Many physical and mathematicianshave studied it's physical property and mathematical theory deeply and ob-tained plenteous result.In this dissertation, we aim to study global attractor for three dimensionalGinzburg-Landau equation and the estimate of the dimensionality of ti's at-tractor,the equation as following:u_t=ρu+(1+iγ)â–³u-(1+iμ)|u|^2σu,u(0,x)=u₀(x), x∈Ωu(x,t) isΩ-periodic,Ω=(0, L₁)×(0, L₁)×(0, L₁)∈Ω。where u(t) is an unknown complex function which is defined in three dimen-sional space R³⁺¹,â–³is a Laplacian operator in R³ ,ρ＞0,γ,μare realparameters.This thesis is composed of two chapters. The first chapter devotes to intro-duce the summarize of the dissertation. we recount about the history, physicalbackground and the present circustance of unlimited dimensional dynamic sys-tem and Ginzburg-Landau equation, introduce some main obtained results.The second chapter is the primary proportion of this paper which composedof four sections.The 2.1 section is the introduction which gives the conditions we will needin order to discuss the problem directly in the following section. In the 2.2 section, we proof that the local solution for this three dimensionalGinzburg-Landau equation is existent and unique.In the 2.3 section, we obtain the existence of global solution for this threedimensional Ginzburg-Landau equation by using the method of priori estimate.In the 2.4 section, we obtain the existence of global attractor for this threedimensional Ginzburg-Landau equation and estimate the dimensionality of thisattractor.