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

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.