Weak solutions to the Ginzburg-Landau model in superconductivity with the Coulomb gauge

摘要

We first prove the uniqueness of weak solutions (psi, A) to the 3-D Ginzburg-Landau model in superconductivity with zero magnetic diffusivity and the Coulomb gauge if (psi, A) is an element of W := {(psi, A vertical bar psi is an element of L-2 (0, T; L-infinity) boolean AND L-2 (0, T; H-1), A is an element of C ([0, T]; L-3)}, which is a critical space for some positive constant T. We also prove the global existence of solutions when psi(0) is an element of L-infinity boolean AND W-2/3,W-3/2 and A(0) is an element of L-3. Copyright (C) 2016 JohnWiley & Sons, Ltd.