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

In this paper, we obtain classical solutions of a time-dependent Ginzburg–Landau (TDGL) equations come from the superfluid atomic Fermi gases near the Feshbach resonance from the fermion–boson model. By the properties of Besov and Sobolev spaces and matrix theory, together with the energy method, we establish the global existence and uniqueness of classical solutions of the TDGL equations in the case of BCS-BEC crossover.