Attractors of Modified Coupled Ginzburg–Landau Model

Author:

Chen Shuhong1ORCID,Liu Shuai2

Affiliation:

1. School of Mathematics and Computer, Wuyi University, Wuyishan 354300, Fujian, China

2. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, Fujian, China

Abstract

Bose–Einstein condensation is a gaseous, superfluid state of matter exhibited by bosons as they cool to near absolute zero, which was discovered as early as 1924 but was not experimentally realized until 1995. In 2006, Machida and Koyama developed the corresponding Ginzburg–Landau model for superfluid and Bose–Einstein condensation-spanning phenomena. We mainly consider the global attractor for the initial boundary value problem of the modified coupled Ginzburg–Landau equations, which come from the BCS-BEC crossover model. Combining Gronwall inequality, properties of the binomial function, with some suitable a priori estimates, we establish the existence of global attractors. The attractor results obtained in this paper can provide a strong theoretical basis for the experimental realization of the BCS-BEC spanning phenomenon, and the adopted research method can also serve as a reference for analysing other types of partial differential equation attractors.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Reference23 articles.

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2. Sitzungsberichte der Preussischen akademie der Wissenschaften;A. Einstein;Physikalisch- Mathemathsche Klasse,1924

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5. Classical solutions of time-dependent Ginzburg–Landau theory for atomic Fermi gases near the BCS-BEC crossover

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