The Global Attractor of the 3D Complex GL Equation and the Estimate of its Dimensionality

Abstract:

Article Preview

In three-dimensional space, by using the method of a priori estimation, we have studied the complex-valued GL equation, which has the 2 -th power of the nonlinear term. We have proved that the existence of the global attractor of this equation with the problem of period and border value, and we have studied the dimensionality of Hausdorff and fractal of the global attractor.

Info:

Periodical:

Advanced Materials Research (Volumes 588-589)

Edited by:

Lawrence Lim

Pages:

2051-2054

Citation:

B. T. Li and Z. C. Yuan, "The Global Attractor of the 3D Complex GL Equation and the Estimate of its Dimensionality", Advanced Materials Research, Vols. 588-589, pp. 2051-2054, 2012

Online since:

November 2012

Export:

Price:

$38.00

[1] M.Bartuccelli,P.Constantin,C.Doering,J.D,Gibbon and M.Gisself i h,On the possibility of soft and hard turbulence in the complex Ginzburg—Landau equation[J].Physica D, 1990,(44):421—444.

[2] C.R.Doering,J.D.Gibbon and C.D.Levermore,Weak and strong solutions of the complex Ginzburg—Landau equation[J].Phys D,1994,(71):285—318.

[3] A.Mielke,The complex Ginzburg—Landau equation on large and unbounded domains: sharper bounds and attractors[J].Nonlinearity,1 997,(10):199—222.

DOI: https://doi.org/10.1088/0951-7715/10/1/014

[4] LI Dong-long.Global existence and uniqueness of solution for complex Ginzburg Landau equation in three dimensions [J].Colleges and Universities applied mathematics Journal A clips, 2004,19(4):409—416.

[5] R.Temam. Infinite Dimensional Dynamitic systems in Mechanics and Physics[M]. New York: Springer, 1988.