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Journal of Partial Differential Equations

On the Cauchy Problem of the Ginzburg-Landau Equations for Atomic Fermi Gases Near the BCS-BEC Crossover

Shuhong Chen, Boling Guo

Published Aug 12, 2009• 5 citations
Publisher

Abstract

In this paper we investigate time-dependent Ginzburg-Landau equations come from the superfluid atomic Fermi-gases near the Feshbach resonance from the Fermion-Boson model. We obtain the global existence and uniqueness of solution to the equations in various spatial dimensions.
DOI
10.4208/jpde.v22.n3.3

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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.