Fourier spectral approximations to the dynamics of 3D fractional complex Ginzburg-Landau equation

Hong Lu; Shujuan Lü; Mingji Zhang

doi:10.3934/dcds.2017109

Article Contents

2017, Volume 37, Issue 5: 2539-2564. Doi: 10.3934/dcds.2017109

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Fourier spectral approximations to the dynamics of 3D fractional complex Ginzburg-Landau equation

1.
School of Mathematics and Statistics, Shandong University, Weihai 264209, China
2.
School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
3.
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA

Received: July 2015

Revised: December 2016

Published: May 2017

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Abstract

We study the fractional complex Ginzburg-Landau equation with periodic initial boundary value condition in three spatial dimensions. The problem is discretized fully by Fourier Galerkin spectral method. The dynamical behavior of the resulting discrete system is examined. The existence of a global attractor is established, and the corresponding convergence is proved through the error estimates of the discrete solution. Numerical stability and convergence of the discrete scheme are proved.

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Mathematics Subject Classification: Primary: 65M12, 65N30; Secondary: 65N35.

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