In this chapter, we consider the initial value problem of a Ginzburg- Landau equation
with spatial periodicity condition in three dimension. Firstly, In Section 2 we prove the
existence of local solution (see Theorem 2.1). Furthermore, the existence and uniqueness
of global solution are proved by making a prior estimate for solution u(t) (see Theorem
2.2 and 2.3). In Section 3, the existence of global attractor and upper bound estimates for
its Hausdorff dimensions and fractal dimensions are obtained (see Theorem 3.2 and 3.3).
Then, in Section 4 the existence of finite dimensional exponential attractor is proved (see
Theorem 4.2). In Section 5, we construct a fully discrete Fourier spectral approximation
scheme for problem (1.4)-(1.6) and then prove the existence and convergence of approximate
attractors (see Theorem 5.2.1 and 5.3.2) are presented. Moreover, the long-time