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

摘要

We first prove the uniqueness of weak solutions (psi, A) to the 3-D Ginzburg-Landau system in superconductivity with the temporal gauge if (psi, A). W := {(psi, A)vertical bar psi is an element of L-2(0, T; L-infinity), del psi is an element of L-2(0, T; L-3), 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 for the Ginzburg-Landau system with magnetic diffusivity mu > 0 or mu = 0. Finally, we prove the uniform bounds with respect to mu of strong solutions in space dimensions d = 2. Consequently, the existence of the limit as mu -> 0 can be established.