Uniqueness of weak solutions in critical space of the 3-D time-dependent Ginzburg-Landau equations for superconductivity

摘要

We prove the uniqueness of weak solutions of the 3-D time-dependent Ginzburg-Landau equations for superconductivity with initial data (ψ_0, A_0) ∈ L~2 under the hypothesis that (ψ, A) ∈ L~s (0, T; L~(r, ∞)) × L~s (0, T; L~(r, ∞)) with Coulomb gauge for any (r, s) and (r{top}-, s{top}-) satisfying 2/s + 3/r = 1, 2/s + 3/r=1, s{top}- ≥ (2s)/(s-2), r{top}-≥ (2r)/(r-2) and 3