Local Well-Posedness of Classical Solutions to the Time-Dependent Ginzburg–Landau Model for Superconductivity in Rn

In this paper, we prove the local well-posedness of classical solutions (ψ,A,ϕ) to the nD(n≥3) time-dependent Ginzburg–Landau model in superconductivity with the choice of Coulomb gauge and the main assumptions ψ0,A0∈Hs(Rn) with divA0=0 in Rn and s>n2. This result can be used in the proof of regularity criterion and global-in-time well-posedness of the strong solution.