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

We prove the uniqueness of weak solutions of the 3-D time-dependent Ginzburg-Landau equations for super-conductivity with initial data (ψ0, A0)∈ L2 under the hypothesis that (ψ, A) ∈ Ls(0, T; Lr,∞) ×(0, T; with Coulomb gauge for any (r, s) and satisfying + = 1, + = 1, ≥ , ≥ and 3 < r ≤ 6, 3 < ≤ ∞. Here Lr,∞ ≡ is the Lorentz space. As an application, we prove a uniqueness result with periodic boundary condition when ψ0 ∈ , A0 ∈ L3 (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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