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Nonlinear Analysis

Global attractor for the initial–boundary value problems for Ginzburg–Landau equations for atomic Fermi gases near the BCS–BEC crossover

Shaomei Fang, Lingyu Jin, Boling Guo

Published Feb 1, 2010• 6 citations
Publisher
DOI
10.1016/j.na.2010.01.037

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The present article studies the dynamic behaviour of the time-dependent Ginzburg-Landau equation, which describes the phenomenon of BCS-BEC crossover.First, the appropriate prior estimates are established by Gronwall's inequality and Gagliardo-Nirenberg interpolation inequality, etc.Then, we prove the existence of the global attractor in the time-dependent Ginzburg-Landau system.Finally, the evolution of the field and the influence of physical parameters on the dynamic behaviour are demonstrated by numerical experiments, thereby validating the theory in this article.

Current Science•Nov 25, 2025•0 citations
The present article studies the dynamic behaviour of the time-dependent Ginzburg-Landau equation, which describes the phenomenon of BCS-BEC crossover.First, the appropriate prior estimates are established by Gronwall's inequality and Gagliardo-Nirenberg interpolation inequality, etc.Then, we prove the existence of the global attractor in the time-dependent Ginzburg-Landau system.Finally, the evolution of the field and the influence of physical parameters on the dynamic behaviour are demonstrated by numerical experiments, thereby validating the theory in this article.